Torsional Deformation of Nonrelativistic String Theory

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.

37 pages; v2: published version

References in corpus (5)

• Double Field Theory
• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• Newton-Hooke Algebras, Non-relativistic Branes and Generalized pp-wave Metrics
• Extended Galilean symmetries of non-relativistic strings
• A Non-Relativistic Limit of NS-NS Gravity

Cited by in corpus (13)

• Aspects of Nonrelativistic Strings
• Torsional string Newton-Cartan geometry for non-relativistic strings
• Non-Relativistic Ten-Dimensional Minimal Supergravity
• On the Non-Relativistic Expansion of Closed Bosonic Strings
• Dual D-Brane Actions in Nonrelativistic String Theory
• Nonrelativistic Approximations of Closed Bosonic String Theory
• Generalized Newton-Cartan Geometries for Particles and Strings
• KLT Factorization of Nonrelativistic String Amplitudes
• The Panorama of Spin Matrix Theory
• Spin Matrix Theory in near $\frac{1}{8}$-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• Coset space actions for nonrelativistic strings
• Nonrelativistic strings and the limits of $\mathcal{N}=2$ dualities
• Holographic duals of $\mathcal{N}=1$ quivers in 5d and their nonrelativistic limits