Background field method for nonlinear sigma models in nonrelativistic string theory

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.

Nonrelativistic open string and Yang-Mills theory

“…Turning on such a λλ term would drive the nonlinear sigma model towards the one that describes relativistic string theory. See [14,27] for details. 14 Sometimes it is useful to rewrite the string action using the field redefinitions [7]…”

“…In this latter case, a λλ term in the sigma model will in general be generated by quantum corrections [14]. However, it is possible to relax the condition (3.6) to be E µ A E ν B D [µ τ ν] A = 0 without generating a λλ operator at all loops in the two-dimensional worldsheet sigma model (which can be shown, for example, by using the method in [27]). The condition…”

“…A covariant expansion with respect to ξ µ (X) for the closed string action, i.e. the bulk part in (3.24), has been put forward in [27], where λ and λ are also split into a classical and quantum part as…”

“…However, the full expression of J rI in (3.59) is needed for maintaining the gauge invariance when the beta-functions are concerned. See related discussions for the closed string beta-functions in [27].…”

Lie algebra expansion and integrability in superstring Sigma-models

“…Other non-relativistic theories have been discussed e.g. in [27][28][29], and aspects such as the equations of motion, T-duality transformations, and the identification of the spacetime geometry, dubbed as string Newton-Cartan geometry and its coupling to matter, have received a growing attention [16,18,[30][31][32][33]. Classifying non-relativistic spacetime geometries is also an active field of research [34][35][36].…”