Beta functions for the duality-invariant sigma model

TL;DR

This paper computes the one-loop beta functions and Weyl anomaly for an $O(d,d)$ invariant sigma model, linking anomaly cancellation to the equations of motion of a known string effective action.

Contribution

It provides a detailed calculation of beta functions for the duality-invariant sigma model and connects anomaly cancellation conditions to string theory equations of motion.

Findings

Vanishing Weyl anomaly implies Maharana-Schwarz equations of motion.

Provides a self-contained introduction to beta functions and Weyl anomaly techniques.

Sets groundwork for higher-loop and $\alpha'$ correction studies.

Abstract

The $O(d,d)$ invariant worldsheet theory for bosonic string theory with $d$ abelian isometries is employed to compute the beta functions and Weyl anomaly at one-loop. We show that vanishing of the Weyl anomaly coefficients implies the equations of motion of the Maharana-Schwarz action. We give a self-contained introduction into the required techniques, including beta functions, the Weyl anomaly for two-dimensional sigma models and the background field method. This sets the stage for a sequel to this paper on generalizations to higher loops and $\alpha'$ corrections.