Non equivalence of Carroll limits in relativistic string theory

TL;DR

This paper explores how Carroll limits of relativistic string theories lead to non-equivalent string models with different degrees of freedom, highlighting the effects of singular variable redefinitions.

Contribution

It demonstrates that Carroll limits can produce non-equivalent string theories with distinct degrees of freedom, due to singular transformations affecting configuration space and Lagrangians.

Findings

Carroll strings differ from their relativistic counterparts in degrees of freedom.

Singular redefinitions cause non-equivalence of theories after Carroll limit.

Different Carroll strings emerge depending on the initial relativistic theory.

Abstract

We construct new Carroll strings in flat space by considering the Carroll limit of equivalent relativistic string theories at classical level. In the limit these Carroll strings are no longer equivalent and have different degrees of freedom. This fact is due to a general phenomenon that the configuration space and canonical Lagrangians are no longer equivalent after a singular redefinition of the variables and of the parameters of the starting Lagrangians.