Extended Galilean symmetries of non-relativistic strings

TL;DR

This paper explores the extended Galilean symmetries of two types of non-relativistic strings derived from relativistic limits, revealing infinite-dimensional symmetry structures and associated conserved charges.

Contribution

It identifies and characterizes the extended symmetry algebras of non-relativistic strings, including their infinite-dimensional nature and conserved quantities.

Findings

Non-relativistic strings exhibit extended infinite-dimensional symmetries.

Two sets of non-relativistic Killing equations are derived and solved.

Conserved charges and possible non-central extensions are discussed.

Abstract

We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.