| 1. |
- Azevedo, Tholes, et al.
(författare)
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Heterotic and bosonic string amplitudes via field theory
- 2018
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer. - 1126-6708 .- 1029-8479. ; :10
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Tidskriftsartikel (refereegranskat)abstract
- Previous work has shown that massless tree amplitudes of the type I and IIA/B superstrings can be dramatically simplified by expressing them as double copies between field-theory amplitudes and scalar disk/sphere integrals, the latter containing all the alpha'-corrections. In this work, we pinpoint similar double-copy constructions for the heterotic and bosonic string theories using an alpha'-dependent field theory and the same disk/sphere integrals. Surprisingly, this field theory, built out of dimension-six operators such as (D mu F mu v)(2), has previously appeared in the double-copy construction of conformal supergravity. We elaborate on the alpha' -> infinity limit in this picture and derive new amplitude relations for various gauge-gravity theories from those of the heterotic string.
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| 2. |
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| 3. |
- Berg, Marcus, 1973-, et al.
(författare)
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String-motivated one-loop amplitudes in gauge theories with half-maximal supersymmetry
- 2017
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer. - 1126-6708 .- 1029-8479. ; :7
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Tidskriftsartikel (refereegranskat)abstract
- We compute one-loop amplitudes in six-dimensional Yang-Mills theory with half-maximal supersymmetry from first principles: imposing gauge invariance and locality on an ansatz made from string-theory inspired kinematic building blocks yields unique expressions for the 3- and 4-point amplitudes. We check that the results are reproduced in the field-theory limit alpha' -> 0 of string amplitudes in K3 orbifolds, using simplifications made in a companion string-theory paper.
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| 4. |
- Britto, Ruth, et al.
(författare)
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Coaction and double-copy properties of configuration-space integrals at genus zero
- 2021
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :5
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Tidskriftsartikel (refereegranskat)abstract
- We investigate configuration-space integrals over punctured Riemann spheres from the viewpoint of the motivic Galois coaction and double-copy structures generalizing the Kawai-Lewellen-Tye (KLT) relations in string theory. For this purpose, explicit bases of twisted cycles and cocycles are worked out whose orthonormality simplifies the coaction. We present methods to efficiently perform and organize the expansions of configuration-space integrals in the inverse string tension α′ or the dimensional-regularization parameter ϵ of Feynman integrals. Generating-function techniques open up a new perspective on the coaction of multiple polylogarithms in any number of variables and analytic continuations in the unintegrated punctures. We present a compact recursion for a generalized KLT kernel and discuss its origin from intersection numbers of Stasheff polytopes and its implications for correlation functions of two-dimensional conformal field theories. We find a non-trivial example of correlation functions in (p, 2) minimal models, which can be normalized to become uniformly transcendental in the p → ∞ limit.
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| 5. |
- Broedel, Johannes, et al.
(författare)
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Two dialects for KZB equations : generating one-loop open-string integrals
- 2020
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Ingår i: Journal of High Energy Physics (JHEP). - : SPRINGER. - 1126-6708 .- 1029-8479. ; :12
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Tidskriftsartikel (refereegranskat)abstract
- Two different constructions generating the low-energy expansion of genus-one configuration-space integrals appearing in one-loop open-string amplitudes have been put forward in refs. [1-3]. We are going to show that both approaches can be traced back to an elliptic system of Knizhnik-Zamolodchikov-Bernard(KZB) type on the twice-punctured torus.We derive an explicit all-multiplicity representation of the elliptic KZB system for a vector of iterated integrals with an extra marked point and explore compatibility conditions for the two sets of algebra generators appearing in the two differential equations.
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| 6. |
- D'Hoker, Eric, et al.
(författare)
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Cyclic products of Szego kernels and spin structure sums. Part I. Hyper-elliptic formulation
- 2023
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :5
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Tidskriftsartikel (refereegranskat)abstract
- The summation over spin structures, which is required to implement the GSO projection in the RNS formulation of superstring theories, often presents a significant impediment to the explicit evaluation of superstring amplitudes. In this paper we discover that, for Riemann surfaces of genus two and even spin structures, a collection of novel identities leads to a dramatic simplification of the spin structure sum. Explicit formulas for an arbitrary number of vertex points are obtained in two steps. First, we show that the spin structure dependence of a cyclic product of Szego kernels (i.e. Dirac propagators for worldsheet fermions) may be reduced to the spin structure dependence of the four-point function. Of particular importance are certain trilinear relations that we shall define and prove. In a second step, the known expressions for the genus-two even spin structure measure are used to perform the remaining spin structure sums. The dependence of the spin summand on the vertex points is reduced to simple building blocks that can already be identified from the two-point function. The hyper-elliptic formulation of genus-two Riemann surfaces is used to derive these results, and its SL(2, DOUBLE-STRUCK CAPITAL C) covariance is employed to organize the calculations and the structure of the final formulas. The translation of these results into the language of Riemann & thetasym;-functions, and applications to the evaluation of higher-point string amplitudes, are relegated to subsequent companion papers.
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| 7. |
- D'Hoker, Eric, et al.
(författare)
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Elliptic modular graph forms. Part I. Identities and generating series
- 2021
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :3
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Tidskriftsartikel (refereegranskat)abstract
- Elliptic modular graph functions and forms (eMGFs) are defined for arbitrary graphs as natural generalizations of modular graph functions and forms obtained by including the character of an Abelian group in their Kronecker-Eisenstein series. The simplest examples of eMGFs are given by the Green function for a massless scalar field on the torus and the Zagier single-valued elliptic polylogarithms. More complicated eMGFs are produced by the non-separating degeneration of a higher genus surface to a genus one surface with punctures. eMGFs may equivalently be represented by multiple integrals over the torus of combinations of coefficients of the Kronecker-Eisenstein series, and may be assembled into generating series. These relations are exploited to derive holomorphic subgraph reduction formulas, as well as algebraic and differential identities between eMGFs and their generating series.
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| 8. |
- D'Hoker, Eric, et al.
(författare)
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Identities among higher genus modular graph tensors
- 2022
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Ingår i: Communications in Number Theory and Physics. - : INT PRESS BOSTON, INC. - 1931-4523 .- 1931-4531. ; 16:1, s. 35-74
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Tidskriftsartikel (refereegranskat)abstract
- Higher genus modular graph tensors map Feynman graphs to functions on the Torelli space of genus-h compact Riemann surfaces which transform as tensors under the modular group Sp(2h, Z), thereby generalizing a construction of Kawazumi. An infinite family of algebraic identities between one-loop and tree-level modular graph tensors are proven for arbitrary genus and arbitrary tensorial rank. We also derive a family of identities that apply to modular graph tensors of higher loop order.
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| 9. |
- D'Hoker, Eric, et al.
(författare)
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Two-loop superstring five-point amplitudes. Part I. Construction via chiral splitting and pure spinors
- 2020
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Ingår i: Journal of High Energy Physics (JHEP). - : SPRINGER. - 1126-6708 .- 1029-8479. ; :8
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Tidskriftsartikel (refereegranskat)abstract
- The full two-loop amplitudes for five massless states in Type II and Heterotic superstrings are constructed in terms of convergent integrals over the genus-two moduli space of compact Riemann surfaces and integrals of Green functions and Abelian differentials on the surface. The construction combines elements from the BRST cohomology of the pure spinor formulation and from chiral splitting with the help of loop momenta and homology invariance. The alpha '-> 0 limit of the resulting superstring amplitude is shown to be in perfect agreement with the previously known amplitude computed in Type II supergravity. Investigations of the alpha ' expansion of the Type II amplitude and comparisons with predictions from S-duality are relegated to a first companion paper. A construction from first principles in the RNS formulation of the genus-two amplitude with five external NS states is relegated to a second companion paper.
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| 10. |
- D'Hoker, Eric, et al.
(författare)
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Two-loop superstring five-point amplitudes. Part II. Low energy expansion and S-duality
- 2021
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :2
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Tidskriftsartikel (refereegranskat)abstract
- In an earlier paper, we constructed the genus-two amplitudes for five external massless states in Type II and Heterotic string theory, and showed that the alpha ' expansion of the Type II amplitude reproduces the corresponding supergravity amplitude to leading order. In this paper, we analyze the effective interactions induced by Type IIB superstrings beyond supergravity, both for U(1)(R)-preserving amplitudes such as for five gravitons, and for U(1)(R)-violating amplitudes such as for one dilaton and four gravitons. At each order in alpha ', the coefficients of the effective interactions are given by integrals over moduli space of genus-two modular graph functions, generalizing those already encountered for four external massless states. To leading and sub-leading orders, the coefficients of the effective interactions (DR5)-R-2 and (DR5)-R-4 are found to match those of (DR4)-R-4 and (DR4)-R-6, respectively, as required by non-linear supersymmetry. To the next order, a (DR5)-R-6 effective interaction arises, which is independent of the supersymmetric completion of (DR4)-R-8, and already arose at genus one. A novel identity on genus-two modular graph functions, which we prove, ensures that up to order (DR5)-R-6, the five-point amplitudes require only a single new modular graph function in addition to those needed for the four-point amplitude. We check that the supergravity limit of U(1)(R)-violating amplitudes is free of UV divergences to this order, consistently with the known structure of divergences in Type IIB supergravity. Our results give strong consistency tests on the full five-point amplitude, and pave the way for understanding S-duality beyond the BPS-protected sector.
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| 11. |
- D'Hoker, Eric, et al.
(författare)
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Two-loop superstring five-point amplitudes. Part III. Construction via the RNS formulation : even spin structures
- 2021
-
Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :12
-
Tidskriftsartikel (refereegranskat)abstract
- The contribution from even spin structures to the genus-two amplitude for five massless external NS states in Type II and Heterotic superstrings is evaluated from first principles in the RNS formulation. Using chiral splitting with the help of loop momenta this problem reduces to the evaluation of the corresponding chiral amplitude, which is carried out using the same techniques that were used for the genus-two amplitude with four external NS states. The results agree with the parity-even NS components of a construction using chiral splitting and pure spinors given in earlier companion papers [29] and [33].
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| 12. |
- Dorigoni, Daniele, et al.
(författare)
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Modular graph forms from equivariant iterated Eisenstein integrals
- 2022
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer. - 1126-6708 .- 1029-8479. ; :12
-
Tidskriftsartikel (refereegranskat)abstract
- The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms called modular graph forms. Their differential and number-theoretic properties motivated Brown's alternative construction of non-holomorphic modular forms in the recent mathematics literature from so-called equivariant iterated Eisenstein integrals. In this work, we provide the first validations beyond depth one of Brown's conjecture that equivariant iterated Eisenstein integrals contain modular graph forms. Apart from a variety of examples at depth two and three, we spell out the systematics of the dictionary and make certain elements of Brown's construction fully explicit to all orders.
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| 13. |
- Dorigoni, Daniele, et al.
(författare)
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Poincare series for modular graph forms at depth two. Part I. Seeds and Laplace systems
- 2022
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :1
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Tidskriftsartikel (refereegranskat)abstract
- We derive new Poincare-series representations for infinite families of non-holomorphic modular invariant functions that include modular graph forms as they appear in the low-energy expansion of closed-string scattering amplitudes at genus one. The Poincare series are constructed from iterated integrals over single holomorphic Eisenstein series and their complex conjugates, decorated by suitable combinations of zeta values. We evaluate the Poincare sums over these iterated Eisenstein integrals of depth one and deduce new representations for all modular graph forms built from iterated Eisenstein integrals at depth two. In a companion paper, some of the Poincare sums over depth-one integrals going beyond modular graph forms will be described in terms of iterated integrals over holomorphic cusp forms and their L-values.
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| 14. |
- Dorigoni, Daniele, et al.
(författare)
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Poincare series for modular graph forms at depth two. Part II. Iterated integrals of cusp forms
- 2022
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :1
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Tidskriftsartikel (refereegranskat)abstract
- We continue the analysis of modular invariant functions, subject to inhomogeneous Laplace eigenvalue equations, that were determined in terms of Poincare series in a companion paper. The source term of the Laplace equation is a product of (derivatives of) two non-holomorphic Eisenstein series whence the modular invariants are assigned depth two. These modular invariant functions can sometimes be expressed in terms of single-valued iterated integrals of holomorphic Eisenstein series as they appear in generating series of modular graph forms. We show that the set of iterated integrals of Eisenstein series has to be extended to include also iterated integrals of holomorphic cusp forms to find expressions for all modular invariant functions of depth two. The coefficients of these cusp forms are identified as ratios of their L-values inside and outside the critical strip.
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| 15. |
- Edison, Alex, et al.
(författare)
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One-loop correlators and BCJ numerators from forward limits
- 2020
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Ingår i: Journal of High Energy Physics (JHEP). - : SPRINGER. - 1126-6708 .- 1029-8479. ; :9
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Tidskriftsartikel (refereegranskat)abstract
- We present new formulas for one-loop ambitwistor-string correlators for gauge theories in any even dimension with arbitrary combinations of gauge bosons, fermions and scalars running in the loop. Our results are driven by new all-multiplicity expressions for tree-level two-fermion correlators in the RNS formalism that closely resemble the purely bosonic ones. After taking forward limits of tree-level correlators with an additional pair of fermions/bosons, one-loop correlators become combinations of Lorentz traces in vector and spinor representations. Identities between these two types of traces manifest all supersymmetry cancellations and the power counting of loop momentum. We also obtain parity-odd contributions from forward limits with chiral fermions. One-loop numerators satisfying the Bern-Carrasco-Johansson (BCJ) duality for diagrams with linearized propagators can be extracted from such correlators using the well-established tree-level techniques in Yang-Mills theory coupled to biadjoint scalars. Finally, we obtain streamlined expressions for BCJ numerators up to seven points using multiparticle fields.
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| 16. |
- Edison, Alex, et al.
(författare)
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One-loop matrix elements of effective superstring interactions : α'-expanding loop integrands
- 2021
-
Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :12
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Tidskriftsartikel (refereegranskat)abstract
- In the low-energy effective action of string theories, non-abelian gauge interactions and supergravity are augmented by infinite towers of higher-mass-dimension operators. We propose a new method to construct one-loop matrix elements with insertions of operators D2k Fn and D2k Rn in the tree-level effective action of type-I and type-II superstrings. Inspired by ambitwistor string theories, our method is based on forward limits of moduli-space integrals using string tree-level amplitudes with two extra points, expanded in powers of the inverse string tension α′. Similar to one-loop ambitwistor computations, intermediate steps feature non-standard linearized Feynman propagators which eventually recombine to conventional quadratic propagators. With linearized propagators the loop integrand of the matrix elements obey one-loop versions of the monodromy and KLT relations. We express a variety of four- and five-point examples in terms of quadratic propagators and formulate a criterion on the underlying genus-one correlation functions that should make this recombination possible at all orders in α′. The ultraviolet divergences of the one-loop matrix elements are crosschecked against the non-separating degeneration of genus-one integrals in string amplitudes. Conversely, our results can be used as a constructive method to determine degenerations of elliptic multiple zeta values and modular graph forms at arbitrary weight.
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| 17. |
- Edison, Alex, et al.
(författare)
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One-loop matrix elements of effective superstring interactions : alpha '-expanding loop integrands
- 2021
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :12
-
Tidskriftsartikel (refereegranskat)abstract
- In the low-energy effective action of string theories, non-abelian gauge interactions and supergravity are augmented by infinite towers of higher-mass-dimension operators. We propose a new method to construct one-loop matrix elements with insertions of operators (DFn)-F-2k and (DRn)-R-2k in the tree-level effective action of type-I and type-II superstrings. Inspired by ambitwistor string theories, our method is based on forward limits of moduli-space integrals using string tree-level amplitudes with two extra points, expanded in powers of the inverse string tension alpha'. Similar to one-loop ambitwistor computations, intermediate steps feature non-standard linearized Feynman propagators which eventually recombine to conventional quadratic propagators. With linearized propagators the loop integrand of the matrix elements obey one-loop versions of the monodromy and KLT relations. We express a variety of four- and five-point examples in terms of quadratic propagators and formulate a criterion on the underlying genus-one correlation functions that should make this recombination possible at all orders in alpha'. The ultraviolet divergences of the one-loop matrix elements are crosschecked against the non-separating degeneration of genus-one integrals in string amplitudes. Conversely, our results can be used as a constructive method to determine degenerations of elliptic multiple zeta values and modular graph forms at arbitrary weight.
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| 18. |
- Edison, Alex, et al.
(författare)
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Perfecting one-loop BCJ numerators in SYM and supergravity
- 2023
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :2
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Tidskriftsartikel (refereegranskat)abstract
- We take a major step towards computing D-dimensional one-loop amplitudes in general gauge theories, compatible with the principles of unitarity and the color-kinematics duality. For n-point amplitudes with either supersymmetry multiplets or generic non-supersymmetric matter in the loop, simple all-multiplicity expressions are obtained for the maximal cuts of kinematic numerators of n-gon diagrams. At n = 6, 7 points with maximal supersymmetry, we extend the cubic-diagram numerators to encode all contact terms, and thus solve the long-standing problem of simultaneously realizing the following properties: color-kinematics duality, manifest locality, optimal power counting of loop momenta, quadratic rather than linearized Feynman propagators, compatibility with double copy as well as all graph symmetries. Color-kinematics dual representations with similar properties are presented in the half-maximally supersymmetric case at n = 4, 5 points. The resulting gauge-theory integrands and their supergravity counterparts obtained from the double copy are checked to reproduce the expected ultraviolet divergences.
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| 19. |
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| 20. |
- Garozzo, Lucia M., et al.
(författare)
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Berends-Giele currents in Bern-Carrasco-Johansson gauge for F3- and F4-deformed Yang-Mills amplitudes
- 2019
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; :2
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Tidskriftsartikel (refereegranskat)abstract
- We construct new representations of tree-level amplitudes in D-dimensional gauge theories with deformations via higher-mass-dimension operators α′F3 and α′2F4. Based on Berends-Giele recursions, the tensor structure of these amplitudes is compactly organized via off-shell currents. On the one hand, we present manifestly cyclic representations, where the complexity of the currents is systematically reduced. On the other hand, the duality between color and kinematics due to Bern, Carrasco and Johansson is manifested by means of non-linear gauge transformations of the currents. We exploit the resulting notion of Bern-Carrasco-Johansson gauge to provide explicit and manifestly local double-copy representations for gravitational amplitudes involving α′R2 and α′2R3 operators.
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| 21. |
- Gerken, Jan E., et al.
(författare)
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All-order differential equations for one-loop closed-string integrals and modular graph forms
- 2020
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Ingår i: Journal of High Energy Physics (JHEP). - : SPRINGER. - 1126-6708 .- 1029-8479. ; :1
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Tidskriftsartikel (refereegranskat)abstract
- We investigate generating functions for the integrals over world-sheet tori appearing in closed-string one-loop amplitudes of bosonic, heterotic and type-II theories. These closed-string integrals are shown to obey homogeneous and linear differential equations in the modular parameter of the torus. We spell out the first-order Cauchy-Riemann and second-order Laplace equations for the generating functions for any number of external states. The low-energy expansion of such torus integrals introduces infinite families of non-holomorphic modular forms known as modular graph forms. Our results generate homogeneous first- and second-order differential equations for arbitrary such modular graph forms and can be viewed as a step towards all-order low-energy expansions of closed-string integrals.
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| 22. |
- Gerken, Jan E., et al.
(författare)
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Generating series of all modular graph forms from iterated Eisenstein integrals
- 2020
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; 2020:7
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Tidskriftsartikel (refereegranskat)abstract
- We study generating series of torus integrals that contain all so-called modular graph forms relevant for massless one-loop closed-string amplitudes. By analysing the differential equation of the generating series we construct a solution for their low-energy expansion to all orders in the inverse string tension alpha '. Our solution is expressed through initial data involving multiple zeta values and certain real-analytic functions of the modular parameter of the torus. These functions are built from real and imaginary parts of holomorphic iterated Eisenstein integrals and should be closely related to Brown's recent construction of real-analytic modular forms. We study the properties of our real-analytic objects in detail and give explicit examples to a fixed order in the alpha ' -expansion. In particular, our solution allows for a counting of linearly independent modular graph forms at a given weight, confirming previous partial results and giving predictions for higher, hitherto unexplored weights. It also sheds new light on the topic of uniform transcendentality of the alpha ' -expansion.
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| 23. |
- Gerken, Jan, 1991, et al.
(författare)
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Towards closed strings as single-valued open strings at genus one
- 2022
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Ingår i: Journal of Physics A: Mathematical and Theoretical. - : IOP Publishing. - 1751-8121 .- 1751-8113. ; 55:2
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Tidskriftsartikel (refereegranskat)abstract
- We relate the low-energy expansions of world-sheet integrals in genus-one amplitudes of open- and closed-string states. The respective expansion coefficients are elliptic multiple zeta values (eMZVs) in the open-string case and non-holomorphic modular forms dubbed 'modular graph forms (MGFs)' for closed strings. By inspecting the differential equations and degeneration limits of suitable generating series of genus-one integrals, we identify formal substitution rules mapping the eMZVs of open strings to the MGFs of closed strings. Based on the properties of these rules, we refer to them as an elliptic single-valued map which generalizes the genus-zero notion of a single-valued map acting on MZVs seen in tree-level relations between the open and closed string.
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| 24. |
- Guillen, Max, et al.
(författare)
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Scattering Massive String Resonances through Field-Theory Methods
- 2021
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Ingår i: Physical Review Letters. - : American Physical Society. - 0031-9007 .- 1079-7114. ; 127:5
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Tidskriftsartikel (refereegranskat)abstract
- We present a new method, exact in α′, to explicitly compute string tree-level amplitudes involving one massive state and any number of massless ones. This construction relies on the so-called twisted heterotic string, which admits only gauge multiplets, a gravitational multiplet, and a single massive supermultiplet in its spectrum. In this simplified model, we determine the moduli-space integrand of all amplitudes with one massive state using Berends-Giele currents of the gauge multiplet. These integrands are then straightforwardly mapped to gravitational amplitudes in the twisted heterotic string and to the corresponding massive amplitudes of the conventional type-I and type-II superstrings.
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| 25. |
- Mafra, Carlos R., et al.
(författare)
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All Order alpha ' Expansion of One-Loop Open-String Integrals
- 2020
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Ingår i: Physical Review Letters. - : AMER PHYSICAL SOC. - 0031-9007 .- 1079-7114. ; 124:10
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Tidskriftsartikel (refereegranskat)abstract
- We present a new method to evaluate the alpha' expansion of genus-one integrals over open-string punctures and unravel the structure of the elliptic multiple zeta values in its coefficients. This is done by obtaining a simple differential equation of Knizhnik-Zamolodchikov-Bernard-type satisfied by generating functions of such integrals, and solving it via Picard iteration. The initial condition involves the generating functions at the cusp tau -> i infinity and can be reduced to genus-zero integrals.
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| 26. |
- Mafra, Carlos R., et al.
(författare)
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One-loop open-string integrals from differential equations : all-order alpha '-expansions at n points
- 2020
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Ingår i: Journal of High Energy Physics (JHEP). - : SPRINGER. - 1126-6708 .- 1029-8479. ; :3
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Tidskriftsartikel (refereegranskat)abstract
- We study generating functions of moduli-space integrals at genus one that are expected to form a basis for massless n-point one-loop amplitudes of open superstrings and open bosonic strings. These integrals are shown to satisfy the same type of linear and homogeneous first-order differential equation w.r.t. the modular parameter tau which is known from the A-elliptic Knizhnik-Zamolodchikov-Bernard associator. The expressions for their tau-derivatives take a universal form for the integration cycles in planar and non-planar one-loop open-string amplitudes. These differential equations manifest the uniformly transcendental appearance of iterated integrals over holomorphic Eisenstein series in the low-energy expansion w.r.t. the inverse string tension alpha '. In fact, we are led to conjectural matrix representations of certain derivations dual to Eisenstein series. Like this, also the alpha '-expansion of non-planar integrals is manifestly expressible in terms of iterated Eisenstein integrals without referring to twisted elliptic multiple zeta values. The degeneration of the moduli-space integrals at tau -> i infinity is expressed in terms of their genus-zero analogues - (n+2)-point Parke-Taylor integrals over disk boundaries. Our results yield a compact formula for alpha '-expansions of n-point integrals over boundaries of cylinder- or Mobius-strip worldsheets, where any desired order is accessible from elementary operations.
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| 27. |
- Mafra, Carlos R., et al.
(författare)
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Tree-level amplitudes from the pure spinor superstring
- 2023
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Ingår i: Physics reports. - : Elsevier. - 0370-1573 .- 1873-6270. ; 1020, s. 1-162
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Forskningsöversikt (refereegranskat)abstract
- We give a comprehensive review of recent developments on using the pure spinor formalism to compute massless superstring scattering amplitudes at tree level. The main results of the pure spinor computations are placed into the context of related topics including the color-kinematics duality in field theory and the mathematical structure of alphaPRIME-corrections.
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| 28. |
- Porkert, Franziska, et al.
(författare)
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One-loop amplitudes in Einstein-Yang-Mills from forward limits
- 2023
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer. - 1126-6708 .- 1029-8479.
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Tidskriftsartikel (refereegranskat)abstract
- We present a method to compute the integrands of one-loop Einstein-Yang-Mills amplitudes for any number of external gauge and gravity multiplets. Our construction relies on the double-copy structure of Einstein-Yang-Mills as (super-)Yang-Mills with the so-called YM+phi(3) theory - pure Yang-Mills coupled to bi-adjoint scalars - which we implement via one-loop Cachazo-He-Yuan formulae. The YM+phi(3) building blocks are obtained from forward limits of tree-level input in external gluons and scalars, and we give the composition rules for any number of traces and orders in the couplings g and kappa. On the one hand, we spell out supersymmetry- and dimension-agnostic relations that reduce loop integrands of Einstein-Yang-Mills to those of pure gauge theories. On the other hand, we present four-point results for maximal and half-maximal supersymmetry where all supersymmetry cancellations are exposed. In the half-maximal case, we determine six-dimensional anomalies due to chiral hypermultiplets in the loop.
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| 29. |
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| 30. |
- Rodriguez, Carlos, 1992-
(författare)
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Cohomologies for String Amplitudes
- 2024
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we cover methods useful for the low-energy-expansion, or α’-expansion of string amplitudes. The task of α’-expanding a string amplitude can be divided into two steps: decomposing your string amplitude into a family of integrals, and figuring out how to α’-expand each integral in these families. We review such integrals, which we call string integrals, in this thesis.Related to string integrals, we also introduce versions of these integrals were some punctures are not integrated over. We call the resulting integrals stringy integrals, and these are going to be functions of these leftover punctures (and τ in the genus-one case). We characterize these family of stringy integrals at genus-zero and genus-one, which includes knowing what differential equations they satisfy and their α’-expansion. In fact, the differential equation of these integrals is crucial to obtain efficient α’-expansions, as generating functions of multiple polylogarithms or their elliptic counterparts, and highlight mathematical properties these integrals exhibit. We also study such generating functions of multiple polylogarithms in an abstract setting, to better understand properties of polylogarithms themselves.We finalize with some discussion of twisted cohomology, and how it can be used to give a mathematical foundation for some of our families of stringy integrals, making them true bases of integrals. Hence, the title of the thesis. Moreover, we use twisted cohomology at genus-one to find a double-copy formula for some of our stringy integrals, and related them to generating functions of elliptic modular graph forms.
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