Geometry of Nonrelativistic string

TL;DR

This paper formulates nonrelativistic bosonic string theory in curved space using Galilean Gauge theory, establishing a consistent model interacting with gravity through symmetry localization and canonical analysis.

Contribution

It introduces a novel gauge-theoretic approach to nonrelativistic string theory in curved backgrounds, linking symmetry localization with gravitational interactions.

Findings

Derived the nonrelativistic string action in curved space via Galilean Gauge theory.

Performed canonical analysis confirming gauge transformations match diffeomorphisms.

Established consistency between Lagrangian and Hamiltonian formulations.

Abstract

The nonrelativistic bosonic string theory in a curved manifold is formulated here using gauging of symmetry approach ( Galilean Gauge theory ) . The corresponding model in flat space has some global symmetries . By localizing these symmetries as per Galilean Gauge theory , the action for the nonrelativistic string interacting with gravity is obtained. A canonical analysis of the model has been performed which demonstrate that the transformations of the basic field variables under gauge transformations in phase space are equivalent to the diffeomorphism parameters by an exact mapping. Thus complete consistency of our results from both Lagrangian and Hamiltonian procedures are established.