| 1. |
- 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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| 2. |
- 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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| 3. |
- 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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| 4. |
- 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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| 5. |
- 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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| 6. |
- 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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