  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.
