Nonrelativistic string theory sigma model and its canonical formulation

Josef Klusoň

doi:10.1140/epjc/s10052-019-6623-9

Josef Klusoň

Open Access

https://doi.org/10.1140/epjc/s10052-019-6623-9

Copy DOI

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 stringy Newton–Cartan background.

Highlights

Introduction and summaryIn [1,2] non-relativistic string theory with Galilean invariant global symmetry was proposed.1 This theory is described by two-dimensional quantum field theory which is well defined and which contain fields that describe dynamics of string in target space-time together with additional fields which are crucial for consistency of string theory
It is important to stress that the target space-time, where the string propagates corresponds to flat space-time invariant under global stringy Galilean symmetry
Non-relativistic string theory provides a quantization of stringy non-relativistic spacetime geometry in the same way as relativistic string theory provides quantization of Riemannian geometry

Summary

Introduction and summary

In [1,2] non-relativistic string theory with Galilean invariant global symmetry was proposed. This theory is described by two-dimensional quantum field theory which is well defined and which contain fields that describe dynamics of string in target space-time together with additional fields which are crucial for consistency of string theory. In [1,2] non-relativistic string theory with Galilean invariant global symmetry was proposed.. Natural question is whether we can formulate non-linear sigma model that describes string propagation on a non-relativistic target space-time structure. The important step in our canonical formulation of non-relativistic string theory is to perform analysis of T-duality since, as was shown in [17], T-duality of nonrelativistic string theory is more complex than in case of its relativistic version. In Sect. (4) we explicitly solve second class constraint and determine corresponding Hamiltonian

Non-linear sigma model on stringy Newton–Cartan geometry

Hamiltonian formulation of string in stringy Newton–Cartan background

Second class constraints and their solution