Nonrelativistic Open String and Yang-Mills Theory

TL;DR

This paper develops a nonrelativistic open string theory framework, linking it to Galilean invariant gauge theories and deriving equations of motion from conformal invariance conditions in string backgrounds.

Contribution

It constructs a classical and quantum nonrelativistic open string worldsheet theory and connects it to Galilean invariant Yang-Mills and Dirac-Born-Infeld type actions.

Findings

Open string low energy dynamics described by Galilean invariant U(n) Yang-Mills theory.

Nonrelativistic open string excitations with winding are encoded in a higher-dimensional gauge theory.

Derived nonlinear equations of motion from conformal invariance of boundary couplings.

Abstract

The classical and quantum worldsheet theory describing nonrelativistic open string theory in an arbitrary nonrelativistic open and closed string background is constructed. We show that the low energy dynamics of open strings ending on n coincident D-branes in flat spacetime is described by a Galilean invariant U(n) Yang-Mills theory. We also study nonrelativistic open string excitations with winding number and demonstrate that their dynamics can be encoded into a local gauge theory in one higher dimension. By demanding conformal invariance of the boundary couplings, the nonlinear equations of motion that govern the consistent open string backgrounds coupled to an arbitrary closed background (described by a string Newton-Cartan geometry, Kalb-Ramond, and dilaton field) are derived and shown to emerge from a Galilean invariant Dirac-Born-Infeld type action.