Non-relativistic quantum strings from gauged WZW models

TL;DR

This paper constructs non-relativistic quantum string theories using gauged WZW models, employing a null gauging approach and free field realizations to analyze the spectrum and BRST cohomology.

Contribution

It introduces a novel method to derive non-relativistic quantum strings from gauged WZW models with a null gauging technique.

Findings

Derived a closed string theory similar to Gomis--Ooguri string

Computed the Virasoro BRST cohomology for the model

Identified spectrum differences between holomorphic and antiholomorphic sectors

Abstract

We construct non-relativistic quantum strings from gauged Wess--Zumino--Witten (WZW) models. We depart from the fact that Lie groups with a bi-invariant galilean structure can be seen as the quotient by a null central subgroup of a generalised Nappi--Witten group. We implement the quotient by a chiral null gauging. We use a particular free field realisation of the Nappi--Witten current algebra to compute the Virasoro BRST cohomology of the gauged WZW model, resulting in a closed string theory reminiscent of the bosonic Gomis--Ooguri string, but whose spectrum differs slightly between the holomorphic and antiholomorphic sectors.