Bosonization in Non-Relativistic CFTs

TL;DR

This paper explicitly demonstrates the correspondence between protected operators in a non-relativistic bosonization duality involving 2+1 dimensional Chern-Simons theories, highlighting the matching of operators and the duality's limitations.

Contribution

It provides a detailed operator-level matching in a non-relativistic duality, clarifying the mechanism of duality failure for certain flavor numbers.

Findings

Matching of protected operators between dual theories

Identification of duality failure for N_f > N

Non-relativistic setting facilitates duality studies

Abstract

We demonstrate explicitly the correspondence between all protected operators in a 2+1 dimensional non-supersymmetric bosonization duality in the non-relativistic limit. Roughly speaking we consider $SU(N)$ Chern-Simons field theory at level $k$ with $N_f$ flavours of fundamental boson, and match its chiral sector to that of a $SU(k)$ theory at level $N$ with $N_f$ fundamental fermions. We present the matching at the level of indices and individual operators, seeing the mechanism of failure for $N_f > N$, and point out that the non-relativistic setting is a particularly friendly setting for studying interesting questions about such dualities.