Background Field Method for Nonlinear Sigma Models in Nonrelativistic String Theory

TL;DR

This paper develops a covariant background field method for nonrelativistic string theory formulated on string Newton-Cartan geometry, enabling the computation of beta-functions in this non-Riemannian setting.

Contribution

It introduces a covariant background field approach tailored for nonrelativistic string theory in string Newton-Cartan geometry, facilitating beta-function calculations.

Findings

Derived beta-functions for nonrelativistic string sigma models.

Extended the background field method to non-Riemannian geometries.

Provided tools for analyzing quantum consistency of nonrelativistic strings.

Abstract

We continue the study of nonrelativistic string theory in background fields. Nonrelativistic string theory is described by a nonlinear sigma model that maps a relativistic worldsheet to a non-Lorentzian and non-Riemannian target space geometry, which is known to be string Newton-Cartan geometry. We develop the covariant background field method in this non-Riemannian geometry. We apply this background field method to compute the beta-functions of the nonlinear sigma model that describes nonrelativistic string theory on a string Newton-Cartan geometry background, in presence of a Kalb-Ramond two-form and dilaton field.