Aspects of Nonrelativistic Strings

TL;DR

This review summarizes recent advances in nonrelativistic string theory, highlighting its unique non-Lorentzian geometries, spectrum, and connections to other string frameworks, with applications to AdS/CFT and D-branes.

Contribution

It provides a comprehensive overview of nonrelativistic string theory, including target-space geometry, open strings, and applications to decoupling limits and holography.

Findings

Nonrelativistic strings have a Galilean dispersion relation.

The relevant target-space geometry is torsional string Newton-Cartan.

Nonrelativistic string theory connects to matrix string theory and noncommutative open strings.

Abstract

We review recent developments on nonrelativistic string theory. In flat spacetime, the theory is defined by a two-dimensional relativistic quantum field theory with nonrelativistic global symmetries acting on the worldsheet fields. This theory arises as a self-contained corner of relativistic string theory. It has a string spectrum with a Galilean dispersion relation, and a spacetime S-matrix with nonrelativistic symmetry. This string theory also gives a unitary and ultraviolet complete framework that connects different corners of string theory, including matrix string theory and noncommutative open strings. In recent years, there has been a resurgence of interest in the non-Lorentzian geometries and quantum field theories that arise from nonrelativistic string theory in background fields. In this review, we start with an introduction to the foundations of nonrelativistic string theory in flat spacetime. We then give an overview of recent progress, including the appropriate target-space geometry that nonrelativistic strings couple to. This is known as (torsional) string Newton-Cartan geometry, which is neither Lorentzian nor Riemannian. We also give a review of nonrelativistic open strings and effective field theories living on D-branes. Finally, we discuss applications of nonrelativistic strings to decoupling limits in the context of the AdS/CFT correspondence.