Nonrelativistic String Theory Sigma Model and Its Canonical Formulation

TL;DR

The work develops a complete canonical framework for the non-relativistic string sigma model on stringy Newton-Cartan geometry, detailing the full set of primary, secondary, first-class and second-class constraints. By introducing a matrix-valued Newton potential Phi_AB and a boosted inverse hat_tau^mu_A, it constructs the first-class Hamiltonian and diffeomorphism constraints and resolves the second-class sector to obtain an on-shell H_tau that matches the Kluson construction, reinforcing cross-consistency with prior approaches. The Lagrangian reconstructed from the canonical data aligns with the non-relativistic string action of Andringa, after cancellations of Phi_AB-dependent terms. The analysis lays groundwork for further studies, including T-duality on this background.

Abstract

This paper is devoted to the canonical analysis of non-linear sigma model that describes motion of non-relativistic string on stringy Newton-Cartan background. We determine structure of constraints of this string and compare resulting Hamiltonian with previous proposal of non-relativistic string on Newton-Cartan background.