Poisson equation for genus two string invariants: a conjecture

Basu, Anirban

doi:10.1007/jhep04(2021)050

Cited by 6 publications

(5 citation statements)

References 41 publications

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“…This is a subject in which there have been many recent developments both in the theoretical physics literature and the mathematics literature [115][116][117][118][119][120][121][122][123]. See also the reviews [124,125], which cover much more of the literature than we can in this article, [126] for a Mathematica implementation and [127][128][129][130][131][132][133][134][135] for generalisations to higher genus.…”

Section: Modular Graph Forms and Superstring Perturbation Theorymentioning

confidence: 99%

The SAGEX review on scattering amplitudes Chapter 10: Selected topics on modular covariance of type IIB string amplitudes and their N=4 supersymmetric Yang–Mills duals

Dorigoni

Green²,

Wen³

2022

J. Phys. A: Math. Theor.

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This article reviews some results of the SAGEX programme that have developed in the understanding of the interplay of supersymmetry and modular covariance of scattering amplitudes in type IIB superstring theory and its holographic image in N=4 supersymmetric Yang-Mills theory (SYM). The first section includes the determination of exact expressions for BPS interactions in the low-energy expansion of type IIB superstring amplitudes. The second section concerns properties of a certain class of integrated correlators in N=4 SYM with arbitrary classical gauge group that are exactly determined by supersymmetric localisation. Not only do these reproduce known features of perturbative and non-perturbative N=4 SYM for any classical gauge group, but they have large-N expansions that are in accord with expectations based on the holographic correspondence with superstring theory. The final section focusses on modular graph functions. These are modular functions that are closely associated with coefficients in the low-energy expansion of superstring perturbation theory and have recently received quite a lot of interest in both the physics and mathematics literature.

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Section: Modular Graph Forms and Superstring Perturbation Theorymentioning

confidence: 99%

The SAGEX review on scattering amplitudes Chapter 10: Selected topics on modular covariance of type IIB string amplitudes and their N=4 supersymmetric Yang–Mills duals

Dorigoni

Green²,

Wen³

2022

J. Phys. A: Math. Theor.

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“…The fascinating properties of modular graph forms include multiple zeta values in their expansion around the cusp τ → i∞, with τ the modular parameter of the torus, and intricate networks of algebraic and differential relations. Accordingly, the study of MGFs has received considerable attention in both the physics and mathematics literature [33][34][35][36][37][38][39][40][41], also see [42] for a review, [43] for a Mathematica implementation and [44][45][46][47][48][49][50][51][52] for generalisations to higher genus. The direct evaluation of world-sheet integrals in closed-string genus-one amplitudes yields lattice-sum representations of MGFs [1,2,4,5,18].…”

Section: Jhep01(2022)133mentioning

confidence: 99%

Poincaré series for modular graph forms at depth two. Part I. Seeds and Laplace systems

Dorigoni

Kleinschmidt

Schlotterer

2022

J. High Energ. Phys.

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We derive new Poincaré-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 Poincaré 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 Poincaré 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 Poincaré 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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“…Similarly, building blocks of multi-loop closed-string amplitudes led to the definition of higher-genus modular graph functions [189] with applications to the low-energy expansion of two-loop amplitudes at four [190] and five points [185]. In fact, the study of algebraic [185] and differential relations [183,375] among modular graph functions beyond genus one motivates their generalization to modular graph tensors [376]. Motivated in part by a construction of Kawazumi [377,378], modular graph tensors are introduced as non-holomorphic functions on the Torelli space of compact Riemann surfaces of genus g which transform as tensors under the modular group Sp(2g, Z).…”

Section: Mathematical Structuresmentioning

confidence: 99%