A simplifying feature of the heterotic one loop four graviton amplitude

Abstract

We show that the weight four modular graph functions that contribute to the integrand of the t_8 t_8 D^4 R^4 term at one loop in heterotic string theory do not require regularization, and hence the integrand is simple. This is unlike the graphs that contribute to the integrands of the other gravitational terms at this order in the low momentum expansion, and these integrands require regularization. This property persists for an infinite number of terms in the effective action, and their integrands do not require regularization. We find non--trivial relations between weight four graphs of distinct topologies that do not require regularization by performing trivial manipulations using auxiliary diagrams.

arXiv comment16 pages, LaTeX, 9 figures

References in corpus (15)

• Two-Loop Superstrings VI: Non-Renormalization Theorems and the 4-Point Function
• Two loops in eleven dimensions
• Motivic Multiple Zeta Values and Superstring Amplitudes
• The low energy expansion of the one-loop type II superstring amplitude
• On the modular structure of the genus-one Type II superstring low energy expansion
• The closed-string 3-loop amplitude and S-duality
• New Higher-Derivative $R^4$ Theorems
• The Supersymmetric Effective Action of the Heterotic String in Ten Dimensions
• Proving relations between modular graph functions
• Proof of a modular relation between 1-, 2- and 3-loop Feynman diagrams on a torus
• Poisson equation for the Mercedes diagram in string theory at genus one
• Simplifying the one loop five graviton amplitude in type IIB string theory
• Poisson equation for the three loop ladder diagram in string theory at genus one
• Non-BPS interactions from the type II one loop four graviton amplitude
• Hierarchy of Modular Graph Identities

Cited by in corpus (7)

• Exploring transcendentality in superstring amplitudes
• Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings
• Modular graph functions and odd cuspidal functions -- Fourier and Poincaré series
• Eigenvalue equation for the modular graph $C_{a,b,c,d}$
• Holomorphic subgraph reduction of higher-point modular graph forms
• Eigenvalue equation for genus two modular graphs
• Basis Decompositions and a Mathematica Package for Modular Graph Forms