On Anomaly-free Supergravity as an Effective String Theory

TL;DR

This paper demonstrates that anomaly-free supergravity equations satisfy a differential condition akin to Weyl anomaly relations, supporting its role as a complete effective theory for heterotic strings.

Contribution

It establishes a connection between anomaly-free supergravity equations and Weyl anomaly coefficients, suggesting supergravity's completeness as a string effective theory.

Findings

Supergravity equations fulfill a differential condition to all orders in α'

Supports supergravity as a potential complete effective string theory

Links supergravity equations with string sigma model anomalies

Abstract

The equations of motion of anomaly-free supergravity are shown to fulfil (to all orders in $\alpha'$) a differential condition corresponding to the one relating the Weyl anomaly coefficients for a non-linear sigma model representing a (heterotic) string propagating in a non-trivial background. This supports the possibility that anomaly-free supergravity could provide the complete massless effective theory for the heterotic string.