Low momentum expansion of one loop amplitudes in heterotic string theory

Abstract

We consider the low momentum expansion of the four graviton and the two graviton--two gluon amplitudes in heterotic string theory at one loop in ten dimensions, and analyze contributions upto the D^2 R^4 interaction from the four graviton amplitude, and the D^4 R^2 F^2 interaction from the two graviton--two gluon amplitude. The calculations are performed by obtaining equations for the relevant modular graph functions that arise in the modular invariant integrals, and involve amalgamating techniques used in the type II theory and the calculation of the elliptic genus in the heterotic theory.

67 pages, LaTeX, 14 figures

References in corpus (6)

• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• Modular properties of two-loop maximal supergravity and connections with string theory
• $D^6{R}^4$ amplitudes in various dimensions
• Tetrahedral modular graph functions
• The D^6 R^4 term from three loop maximal supergravity
• Supersymmetry Breaking Effects using the Pure Spinor Formalism of the Superstring

Cited by in corpus (6)

• All-order differential equations for one-loop closed-string integrals and modular graph forms
• Generating series of all modular graph forms from iterated Eisenstein integrals
• 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
• Poincaré series for modular graph forms at depth two. I. Seeds and Laplace systems
• To the cusp and back: Resurgent analysis for modular graph functions