Bosonization duality in 2+1 dimensions and critical current correlation functions in Chern-Simons $U(1)\times U(1)$ Abelian Higgs model

TL;DR

This paper explores the duality between a Chern-Simons $U(1)\times U(1)$ Higgs model and a fermionic topological field theory, analyzing critical current correlations and the nature of the phase transition.

Contribution

It provides a detailed analysis of the duality, showing the equivalence of current correlators and confirming the existence of a critical point via fermionic duality and Schwinger-Dyson analysis.

Findings

Current correlators coincide up to a universal factor.

Duality supports the existence of a critical point in the bosonic model.

No dynamical mass generation occurs in the fermionic dual with Chern-Simons term.

Abstract

While the phase structure of the $U(1)\times U(1)$-symmetric Higgs theory is still under debate, a version of this theory with an additional Chern-Simons term was recently shown to undergo a second-order phase transition [V. Shyta, J. van den Brink, and F. S. Nogueira, Phys. Rev. Lett. 127, 045701 (2021)]. This theory is dual to a topological field theory of massless fermions featuring two gauge fields. Here we elaborate on several aspects of this duality, focusing on the critical current correlators and on the nature of the critical point as reflected by the bosonization duality. The current correlators associated to the $U(1)\times U(1)$ symmetry and the topological current are shown to coincide up to a universal prefactor, which we find to be the same for both $U(1)$ and $U(1)\times U(1)$ topological Higgs theories. The established duality offers in addition another way to substantiate the claim about the existence of a critical point in the bosonic Chern-Simons $U(1)\times U(1)$ Higgs model: a Schwinger-Dyson analysis of the fermionic dual model shows that no dynamical mass generation occurs. The same cannot be said for the theory without the Chern-Simons term in the action.