Modular graph forms from equivariant iterated Eisenstein integrals

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.

arXiv comment45 pages; submission includes ancillary data files; v2: typos corrected / minor improvements, matches published version

References in corpus (37)

• The Multiple Zeta Value Data Mine
• Elliptic multiple zeta values and one-loop superstring amplitudes
• Motivic Multiple Zeta Values and Superstring Amplitudes
• The low energy expansion of the one-loop type II superstring amplitude
• Low energy expansion of the four-particle genus-one amplitude in type II superstring theory
• Closed String Amplitudes as Single-Valued Open String Amplitudes
• On the modular structure of the genus-one Type II superstring low energy expansion
• Closed Superstring Amplitudes, Single-Valued Multiple Zeta Values and Deligne Associator
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• All order alpha'-expansion of superstring trees from the Drinfeld associator
• Single-valued integration and superstring amplitudes in genus zero
• Relations between elliptic multiple zeta values and a special derivation algebra
• Higher genus modular graph functions, string invariants, and their exact asymptotics
• Proving relations between modular graph functions
• From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop
• Proof of a modular relation between 1-, 2- and 3-loop Feynman diagrams on a torus
• Closed strings as single-valued open strings: A genus-zero derivation
• All-order differential equations for one-loop closed-string integrals and modular graph forms
• Twisted elliptic multiple zeta values and non-planar one-loop open-string amplitudes
• Superstring amplitudes and the associator
• Generating series of all modular graph forms from iterated Eisenstein integrals
• Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings
• Two-loop superstring five-point amplitudes II: Low energy expansion and S-duality
• Modular graph functions and odd cuspidal functions -- Fourier and Poincaré series
• On the algebraic structure of iterated integrals of quasimodular forms
• The SAGEX Review on Scattering Amplitudes, Chapter 10: Selected topics on modular covariance of type IIB string amplitudes and their $\mathcal{N}=4$ supersymmetric Yang-Mills duals
• Poincaré series for modular graph forms at depth two. II. Iterated integrals of cusp forms
• A note on the Drinfeld associator for genus-zero superstring amplitudes in twisted de Rham theory
• Towards single-valued polylogarithms in two variables for the seven-point remainder function in multi-Regge-kinematics
• Poincaré series for modular graph forms at depth two. I. Seeds and Laplace systems
• Holomorphic subgraph reduction of higher-point modular graph forms
• Elliptic modular graph forms I: Identities and generating series
• Eigenvalue equation for genus two modular graphs
• Universal Mixed Elliptic Motives
• Basis Decompositions and a Mathematica Package for Modular Graph Forms
• Poisson equation for genus two string invariants: a conjecture

Cited by in corpus (9)

• Tree-level amplitudes from the pure spinor superstring
• Bootstrapping spinning two body problem in dynamical Chern-Simons gravity using worldline QFT
• Basis decompositions of genus-one string integrals
• Canonical differential equations and intersection matrices
• Advanced tools for basis decompositions of genus-one string integrals
• Integral of depth zero to three basis of Modular Graph Functions
• Type II superstring amplitude at one-loop and transcendentality
• From Modular Graph Forms to Iterated Integrals
• Modular Features of Superstring Scattering Amplitudes: Generalised Eisenstein Series and Theta Lifts