Non-relativistic quantum strings from gauged WZW models

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.