Dual D-Brane Actions in Nonrelativistic String Theory

TL;DR

This paper develops worldvolume actions for nonrelativistic D-branes in string theory, explores their dualities, and extends the framework to include RR potentials and non-Riemannian geometries like string Newton-Cartan geometry.

Contribution

It introduces dual D-brane actions in nonrelativistic string theory and generalizes string dualities and limits to include RR fields and non-Riemannian geometries.

Findings

Uncovered novel dual D-brane actions via gauge field duality.

Extended string theory limits to include RR potentials and non-Riemannian geometries.

Generalized T-duality rules to nonrelativistic string theory with RR fields.

Abstract

We study worldvolume actions for D-branes coupled to the worldvolume U(1) gauge field and Ramond-Ramond (RR) potentials in nonrelativistic string theory. This theory is a self-contained corner of relativistic string theory and has a string spectrum with a Galilean-invariant dispersion relation. We therefore refer to such D-branes in nonrelativistic string theory as nonrelativistic D-branes. We focus on the bosonic fields in spacetime and also couple the D-branes to general closed string geometry, Kalb-Ramond, and dilaton background fields. We dualize nonrelativistic D-branes by performing a duality transformation on the worldvolume U(1) gauge field and uncover novel dual D-brane actions. This generalizes familiar properties, such as the SL(2,Z) duality in Type IIB superstring theory and the relation between Type IIA superstring and M-theory, to nonrelativistic string and M-theory. Moreover, we generalize the limit of string theory, in which nonrelativistic string theory arises, to include RR potentials. This stringy limit induces a codimension-two foliation structure in spacetime. This spacetime geometry is non-Riemannian and known as string Newton-Cartan geometry. In contrast, nonrelativistic M-theory that we probe by dualizing D2- and D4-branes in nonrelativistic string theory arises as a membrane limit of M-theory, and it is coupled to a membrane Newton-Cartan geometry with a codimension-three foliation structure. We also discuss T-duality in nonrelativistic string theory and generalize Buscher rules from earlier work to include RR potentials.