Non-Lorentzian Ka\v{c}-Moody Algebras

TL;DR

This paper explores non-Lorentzian Kac-Moody algebras in 2D quantum field theories, deriving their structures through contractions and establishing their role in Carrollian and Galilean conformal field theories with new symmetry insights.

Contribution

It introduces a novel non-Lorentzian Kac-Moody algebra framework, deriving associated Sugawara constructions and Knizhnik-Zamolodchikov equations from contraction methods.

Findings

Constructed NLKM algebra via contraction and Carrollian perspective

Derived NL Sugawara and KZ equations from symmetries

Established isomorphism between Galilean and Carrollian algebras

Abstract

We investigate two dimensional (2d) quantum field theories which exhibit Non- Lorentzian Ka\v{c}-Moody (NLKM) algebras as their underlying symmetry. Our investigations encompass both 2d Galilean (speed of light $c \rightarrow \infty$) and Carrollian ($c \rightarrow 0$) CFTs with additional number of infinite non-Abelian currents, stemming from an isomorphism between the two algebras. We alternate between an intrinsic and a limiting analysis. Our NLKM algebra is constructed first through a contraction and then derived from an intrinsically Carrollian perspective. We then go on to use the symmetries to derive a Non-Lorentzian (NL) Sugawara construction and ultimately write down the NL equivalent of the Knizhnik Zamolodchikov equations. All of these are also derived from contractions, thus providing a robust cross-check of our analyses.