T-Duality in Nonrelativistic Open String Theory

TL;DR

This paper investigates T-duality in nonrelativistic open string theory, demonstrating how it relates to relativistic and noncommutative theories within the DLCQ framework, and explores the mapping of their worldvolume dynamics.

Contribution

It provides a detailed analysis of T-duality transformations in nonrelativistic open string theory and shows their connection to relativistic and noncommutative theories in DLCQ.

Findings

T-duality maps nonrelativistic open string theory to relativistic and noncommutative theories.

The worldvolume Dirac-Born-Infeld actions are related through T-duality.

The analysis is performed within the framework of string Newton-Cartan geometry.

Abstract

Nonrelativistic open string theory is defined by a worldsheet theory that produces a Galilean invariant string spectrum and is described at low energies by a nonrelativistic Yang-Mills theory. We study T-duality transformations in the path integral for the sigma model that describes nonrelativistic open string theory coupled to an arbitrary closed string background, described by a string Newton-Cartan geometry, Kalb-Ramond, and dilaton field. We prove that T-duality transformations map nonrelativistic open string theory to relativistic and noncommutative open string theory in the discrete light cone quantization (DLCQ), a quantization scheme relevant for Matrix string theory. We also show how the worldvolume dynamics of nonrelativistic open string theory described by the Dirac-Born-Infeld type action maps to the Dirac-Born-Infeld actions describing the worldvolume theories of the DLCQ of open string theory and noncommutative open string theory.