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.

arXiv comment67 pages, LaTeX, 14 figures

References in corpus (37)

• Effects of D-instantons
• U-duality and M-Theory
• Superstring Scattering from D-Branes
• On $R^4$ threshold corrections in IIB string theory and (p,q) string instantons
• Duality and higher derivative terms in M theory
• Curvature terms in D-brane actions and their M-theory origin
• Two-Loop Superstrings VI: Non-Renormalization Theorems and the 4-Point Function
• Low energy expansion of the four-particle genus-one amplitude in type II superstring theory
• Heterotic / type I duality and D-brane instantons
• Two-loop superstrings and S-duality
• On the modular structure of the genus-one Type II superstring low energy expansion
• The closed-string 3-loop amplitude and S-duality
• Heterotic - type I superstring duality and low-energy effective actions
• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• The Supersymmetric Effective Action of the Heterotic String in Ten Dimensions
• Multiparticle one-loop amplitudes and S-duality in closed superstring theory
• Proving relations between modular graph functions
• Modular properties of two-loop maximal supergravity and connections with string theory
• Poisson equation for the Mercedes diagram in string theory at genus one
• $D^6{R}^4$ amplitudes in various dimensions
• Duality constraints on effective actions
• Invariants and divergences in half-maximal supergravity theories
• Simplifying the one loop five graviton amplitude in type IIB string theory
• Tetrahedral modular graph functions
• The two D6R4 type invariants and their higher order generalisation
• Poisson equation for the three loop ladder diagram in string theory at genus one
• Recursion Relations from Space-time Supersymmetry
• Two-loop vacuum energy for Calabi-Yau orbifold models
• Type I/heterotic duality and M-theory amplitudes
• The D^6 R^4 term from three loop maximal supergravity
• Constraining the D3-brane effective action
• Supersymmetry constraints on the R^4 multiplet in type IIB on T^2
• Supersymmetry Breaking Effects using the Pure Spinor Formalism of the Superstring
• On the Rankin-Selberg method for higher genus string amplitudes
• Non-BPS interactions from the type II one loop four graviton amplitude
• Perturbative type II amplitudes for BPS interactions
• Non--analytic terms from nested divergences in maximal supergravity

Cited by in corpus (14)

• From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop
• Exploring transcendentality in superstring amplitudes
• 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
• 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
• 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
• Eigenvalue equation for the modular graph $C_{a,b,c,d}$
• 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
• 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
• To the cusp and back: Resurgent analysis for modular graph functions