R^4 Couplings in M and Type II Theories

TL;DR

This paper explores R^4 couplings in M and Type II string theories, revealing their relation to supersymmetry, one-loop anomalies, and non-perturbative effects, with new insights into corrections to the Einstein term and hypermultiplet geometry.

Contribution

It identifies a new contribution to the Einstein term proportional to the Euler number and connects it to one-loop corrections in hypermultiplet geometry, supported by string theory calculations.

Findings

New correction to Einstein term proportional to Euler number

Relation between R^4 couplings and one-loop holomorphic anomaly

Universal non-perturbative correction to Type IIB hypermultiplet

Abstract

We discuss several implications of R^4 couplings in M theory when compactified on Calabi-Yau (CY) manifolds. In particular, these couplings can be predicted by supersymmetry from the mixed gauge-gravitational Chern-Simons couplings in five dimensions and are related to the one-loop holomorphic anomaly in four-dimensional N=2 theories. We find a new contribution to the Einstein term in five dimensions proportional to the Euler number of the internal CY threefold, which corresponds to a one-loop correction of the hypermultiplet geometry. This correction is reproduced by a direct computation in type II string theories. Finally, we discuss a universal non-perturbative correction to the type IIB hyper-metric.