| 1. |
- Ahlén, Olof, et al.
(author)
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Fourier coefficients attached to small automorphic representations of SLn (A)
- 2018
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In: Journal of Number Theory. - : Elsevier BV. - 0022-314X .- 1096-1658. ; 192, s. 80-142
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Journal article (peer-reviewed)abstract
- We show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of SLn(A) are completely determined by certain highly degenerate Whittaker coefficients. We give an explicit formula for the Fourier expansion, analogously to the Piatetski-Shapiro–Shalika formula. In addition, we derive expressions for Fourier coefficients associated to all maximal parabolic subgroups. These results have potential applications for scattering amplitudes in string theory.
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| 2. |
- Bao, Ling, 1980, et al.
(author)
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Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons
- 2013
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In: Journal of Physics: Conference Series. - : IOP Publishing. - 1742-6588 .- 1742-6596. ; 462:1
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Conference paper (peer-reviewed)abstract
- Type IIA string theory compactified on a rigid Calabi-Yau threefold gives rise to a classical moduli space that carries an isometric action of U(2, 1). Various quantum corrections break this continuous isometry to a discrete subgroup. Focussing on the case where the intermediate Jacobian of the Calabi-Yau admits complex multiplication by the ring of quadratic imaginary integers script O signd, we argue that the remaining quantum duality group is an arithmetic Picard modular group PU(2, 1; script O signd). Based on this proposal we construct an Eisenstein series invariant under this duality group and study its non-Abelian Fourier expansion. This allows the prediction of non-perturbative effects, notably the contribution of D2- and NS5-brane instantons. The present work extends our previous analysis in 0909.4299 which was restricted to the special case of the Gaussian integers script O sign1 = ℤ[i].
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| 3. |
- Bergshoeff, E. A., et al.
(author)
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E10 and gauged maximal supergravity
- 2009
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In: Journal of High Energy Physics. - : Springer Science and Business Media LLC. - 1029-8479 .- 1126-6708. ; 2009:1, s. 020 (artno)-
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Journal article (peer-reviewed)abstract
- We compare the dynamics of maximal three-dimensional gauged supergravity in appropriate truncations with the equations of motion that follow from a one-dimensional E10/K(E-10) coset model at the first few levels. The constant embedding tensor, which describes gauge deformations and also constitutes an M-theoretic degree of freedom beyond eleven-dimensional supergravity, arises naturally as an integration constant of the geodesic model. In a detailed analysis, we find complete agreement at the lowest levels. At higher levels there appear mismatches, as in previous studies. We discuss the origin of these mismatches.
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| 4. |
- Berman, David S., et al.
(author)
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The gauge structure of generalised diffeomorphisms
- 2013
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In: Journal of High Energy Physics. - 1029-8479 .- 1126-6708. ; 1301:1, s. 64-
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Journal article (peer-reviewed)abstract
- We investigate the generalised diffeomorphisms in M-theory, which are gauge transformations unifying diffeomorphisms and tensor gauge transformations. After giving an En(n)-covariant description of the gauge transformations and their commutators, we show that the gauge algebra is infinitely reducible, i.e., the tower of ghosts for ghosts is infinite. The Jacobiator of generalised diffeomorphisms gives such a reducibility transformation. We give a concrete description of the ghost structure, and demonstrate that the infinite sums give the correct (regularised) number of degrees of freedom. The ghost towers belong to the sequences of rep- resentations previously observed appearing in tensor hierarchies and Borcherds algebras. All calculations rely on the section condition, which we reformulate as a linear condition on the cotangent directions. The analysis holds for n
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| 5. |
- Bossard, Guillaume, et al.
(author)
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Beyond E11
- 2017
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In: Journal of High Energy Physics (JHEP). - : Springer. - 1126-6708 .- 1029-8479. ; :5
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Journal article (peer-reviewed)abstract
- We study the non-linear realisation of E-11 originally proposed by West with particular emphasis on the issue of linearised gauge invariance. Our analysis shows even at low levels that the conjectured equations can only be invariant under local gauge transformations if a certain section condition that has appeared in a different context in the E-11 literature is satisfied. This section condition also generalises the one known from exceptional field theory. Even with the section condition, the E-11 duality equation for gravity is known to miss the trace component of the spin connection. We propose an extended scheme based on an infinite-dimensional Lie superalgebra, called the tensor hierarchy algebra, that incorporates the section condition and resolves the above issue. The tensor hierarchy algebra defines a generalised differential complex, which provides a systematic description of gauge invariance and Bianchi identities. It furthermore provides an E-11 representation for the field strengths, for which we define a twisted first order self-duality equation underlying the dynamics.
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| 6. |
- Bossard, Guillaume, et al.
(author)
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Extended geometry of magical supergravities
- 2023
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In: Journal of High Energy Physics (JHEP). - : Springer. - 1126-6708 .- 1029-8479. ; :5
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Journal article (peer-reviewed)abstract
- We provide, through the framework of extended geometry, a geometrisation of the duality symmetries appearing in magical supergravities. A new ingredient is the general formulation of extended geometry with structure group of non-split real form. A simple diagrammatic rule for solving the section constraint by inspection of the Satake diagram is derived.
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| 7. |
- Bossard, Guillaume, et al.
(author)
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Generalised diffeomorphisms for E9
- 2017
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In: Physical Review D - Particles, Fields, Gravitation and Cosmology. - : American Physical Society. - 2470-0010 .- 2470-0029. ; 96, s. 106022-
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Journal article (peer-reviewed)abstract
- We construct generalised diffeomorphisms for E9 exceptional field theory. The trans- formations, which like in the E8 case contain constrained local transformations, close when acting on fields. This is the first example of a generalised diffeomorphism alge- bra based on an infinite-dimensional Lie algebra and an infinite-dimensional coordi- nate module. As a byproduct, we give a simple generic expression for the invariant tensors used in any extended geometry. We perform a generalised Scherk–Schwarz reduction and verify that our transformations reproduce the structure of gauged supergravity in two dimensions. The results are valid also for other affine algebras.
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| 8. |
- D'Hoker, Eric, et al.
(author)
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Elliptic modular graph forms. Part I. Identities and generating series
- 2021
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In: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :3
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Journal article (peer-reviewed)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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| 9. |
- Dorigoni, Daniele, et al.
(author)
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Modular graph forms from equivariant iterated Eisenstein integrals
- 2022
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In: Journal of High Energy Physics (JHEP). - : Springer. - 1126-6708 .- 1029-8479. ; :12
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Journal article (peer-reviewed)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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| 10. |
- Dorigoni, Daniele, et al.
(author)
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Poincare series for modular graph forms at depth two. Part I. Seeds and Laplace systems
- 2022
-
In: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :1
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Journal article (peer-reviewed)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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