Type I/heterotic duality and M-theory amplitudes

TL;DR

This paper explores dualities between heterotic and type I string theories by analyzing supergravity amplitudes, revealing potential non-perturbative effects and higher derivative interaction protections.

Contribution

It provides a detailed analysis of string dualities through supergravity amplitudes, suggesting mechanisms for protected higher derivative interactions beyond perturbation theory.

Findings

R^4 interactions may have no perturbative corrections beyond one loop.

Non-BPS D-instantons contribute to amplitude corrections.

Duality relations help understand non-perturbative effects in string theory.

Abstract

This paper investigates relationships between low-energy four-particle scattering amplitudes with external gauge particles and gravitons in the E_8 X E_8 and SO(32) heterotic string theories and the type I and type IA superstring theories by considering a variety of tree level and one-loop Feynman diagrams describing such amplitudes in eleven-dimensional supergravity in a Horava--Witten background compactified on a circle. This accounts for a number of perturbative and non-perturbative aspects of low order higher derivative terms in the low-energy expansion of string theory amplitudes, which are expected to be protected by half maximal supersymmetry from receiving corrections beyond one or two loops. It also suggests the manner in which type I/heterotic duality may be realised for certain higher derivative interactions that are not so obviously protected. For example, our considerations suggest that R**4 interactions (where R is the Riemann curvature) might receive no perturbative corrections beyond one loop by virtue of a conspiracy involving contributions from (non-BPS) Z2 D-instantons in the type I and heterotic SO(32) theories.