Torsional Deformation of Nonrelativistic String Theory

TL;DR

This paper explores the properties of nonrelativistic string theory, focusing on its geometric structure, symmetry principles, and how quantum corrections can lead to a flow towards relativistic string models.

Contribution

It introduces a modified symmetry principle for nonrelativistic string theory and analyzes the resulting string Newton-Cartan geometry with torsional constraints.

Findings

Nonrelativistic string theory is unitary and UV complete.

Symmetry breaking can induce RG flow towards relativistic string models.

Proposes a modified symmetry principle for supersymmetrization.

Abstract

Nonrelativistic string theory is a self-contained corner of string theory, with its string spectrum enjoying a Galilean-invariant dispersion relation. This theory is unitary and ultraviolet complete, and can be studied from first principles. In these notes, we focus on the bosonic closed string sector. In curved spacetime, nonrelativistic string theory is defined by a renormalizable quantum nonlinear sigma model in background fields, following certain symmetry principles that disallow any deformation towards relativistic string theory. We review previous proposals of such symmetry principles and propose a modified version that might be useful for supersymmetrizations. The appropriate target-space geometry determined by these local spacetime symmetries is string Newton-Cartan geometry. This geometry is equipped with a two-dimensional foliation structure that is restricted by torsional constraints. Breaking the symmetries that give rise to such torsional constraints in the target space will in general generate quantum corrections to a marginal deformation in the worldsheet quantum field theory. Such a deformation induces a renormalization group flow towards sigma models that describe relativistic strings.