Covariant Computation of the Low Energy Effective Action of the Heterotic Superstring

TL;DR

This paper derives the low energy effective action of the heterotic superstring in superspace by ensuring superconformal invariance at tree and one-loop levels, resulting in a supergravity theory coupled to a tensor multiplet.

Contribution

It provides a covariant derivation of the heterotic superstring's effective action using superspace and superconformal invariance constraints.

Findings

Complete supergravity algebra from tree level invariance

Equations of motion from one-loop invariance

Effective action includes old-minimal supergravity with tensor multiplet

Abstract

We derive the low energy effective action of the heterotic superstring in superspace. This is achieved by coupling the covariantly quantized Green-Schwarz superstring of Berkovits to a curved background and requiring that the sigma model has superconformal invariance at tree level and at one loop in $\a'$. Tree level superconformal invariance yields the complete supergravity algebra, and one-loop superconformal invariance the equations of motion of the low energy theory. The resulting low energy theory is old-minimal supergravity coupled to a tensor multiplet. The dilaton is part of the compensator multiplet.