Poisson equation for the Mercedes diagram in string theory at genus one

Basu, Anirban

doi:10.1088/0264-9381/33/5/055005

Cited by 46 publications

(78 citation statements)

References 36 publications

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“…More specifically, the f (a) ij were found to appear naturally from the spin sums of the RNS formalism [36] and the current algebra of heterotic strings [55]. 6 For these theories, the (n−1)! × (n−1)!…”

Section: Component Integrals and String Amplitudesmentioning

confidence: 99%

All-order differential equations for one-loop closed-string integrals and modular graph forms

2020

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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 secondorder 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. arXiv:1911.03476v2 [hep-th] 21 Jan 2020 F Derivation of component equations at three points 65 F.1 General Cauchy-Riemann component equations at three points 66 F.2 Examples of Cauchy-Riemann component equations at three points 67 F.3 Further examples for Laplace equations at three points 68 -ii -10The subscript of ∇DG aims to avoid confusion with the differential operators of Sections 3.1 and 3.2 and refers to the authors D'Hoker and Green of [9] which initiated the systematic study of relations between modular graph forms via repeated action of (2.59).

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Section: Component Integrals and String Amplitudesmentioning

confidence: 99%

All-order differential equations for one-loop closed-string integrals and modular graph forms

2020

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“…To integrate these modular graph functions over M L we simplify the expressions for the coefficients B (p,q) obtained in (A.4) using the identities between modular graph functions derived systematically in [7] up to weight 6 included. Earlier derivations of some of these identities include [1] for two-loop modular graph functions, [52] for D 4 , [6] for all modular graph functions of weight four and five, [53] for the use of slightly different methods, [54,7,55] for tetrahedral graphs, and [32] for the differential identity for C 2,2,1,1 . A more formal context for the identities between modular graph functions has been developed in [56,57].…”

Section: A2 Identities Between Modular Graph Functionsmentioning

confidence: 99%

Exploring transcendentality in superstring amplitudes

D’Hoker¹,

Green

2019

J. High Energ. Phys.

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It is well known that the low energy expansion of tree-level superstring scattering amplitudes satisfies a suitably defined version of uniform transcendentality. In this paper it is argued that there is a natural extension of this definition that applies to the genus-one four-graviton Type II superstring amplitude to all orders in the lowenergy expansion. To obtain this result, the integral over the genus-one moduli space is partitioned into a region M R surrounding the cusp and its complement M L , and an exact expression is obtained for the contribution to the amplitude from M R . The low-energy expansion of the M R contribution is proven to be free of irreducible multiple zeta-values to all orders. The contribution to the amplitude from M L is computed in terms of modular graph functions up to order D 12 R 4 in the low-energy expansion, and general arguments are used beyond this order to conjecture the transcendentality properties of the M L contributions. Uniform transcendentality of the full amplitude holds provided we assign a non-zero weight to certain harmonic sum functions, an assumption which is familiar from transcendentality assignments in quantum field theory amplitudes.

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“…It might be rewarding to approach the low-energy expansion of superstring loop amplitudes at higher multiplicity with Berends-Giele methods. At the one-loop order, this concerns annulus integrals involving elliptic multiple zeta values [85][86][87] and torus integrals involving modular graph functions [88][89][90][91][92][93][94][95][96].…”

Section: Further Directionsmentioning

confidence: 99%

Non-abelian Z-theory: Berends-Giele recursion for the α ′-expansion of disk integrals

Mafra

Schlotterer

2017

J. High Energ. Phys.

110

159

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We present a recursive method to calculate the α -expansion of disk integrals arising in tree-level scattering of open strings which resembles the approach of Berends and Giele to gluon amplitudes. Following an earlier interpretation of disk integrals as doubly partial amplitudes of an effective theory of scalars dubbed as Z-theory, we pinpoint the equation of motion of Z-theory from the Berends-Giele recursion for its tree amplitudes. A computer implementation of this method including explicit results for the recursion up to order α 7 is made available on the website http://repo.or.cz/BGap.git.

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Poisson equation for the Mercedes diagram in string theory at genus one

Cited by 46 publications

References 36 publications

All-order differential equations for one-loop closed-string integrals and modular graph forms

All-order differential equations for one-loop closed-string integrals and modular graph forms

Exploring transcendentality in superstring amplitudes

Non-abelian Z-theory: Berends-Giele recursion for the α ′-expansion of disk integrals

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