Bose Symmetry and Chiral Decomposition of 2D Fermionic Determinants

TL;DR

This paper demonstrates that Bose symmetry facilitates the chiral decomposition of 2D fermionic determinants without obstructing gauge invariance, offering a new perspective on the Polyakov-Wiegman identity.

Contribution

It introduces a systematic approach using Bose symmetry for chiral decomposition of 2D fermionic determinants and reinterprets the Polyakov-Wiegman identity.

Findings

Bose symmetry enables systematic chiral decomposition.

No obstruction to gauge invariance in the decomposition.

A new interpretation of the Polyakov-Wiegman identity.

Abstract

We show in a precise way, either in the fermionic or its bosonized version, that Bose symmetry provides a systematic way to carry out the chiral decomposition of the two dimensional fermionic determinant. Interpreted properly, we show that there is no obstruction of this decomposition to gauge invariance, as is usually claimed. Finally, a new way of interpreting the Polyakov-Wiegman identity is proposed.