Generalized parity transformations in lattice Chern-Simons theory

TL;DR

This paper introduces generalized parity transformations in lattice Chern-Simons theory that preserve the odd behavior of the regularized action, akin to Ginsparg-Wilson relations in chiral symmetry, providing a new symmetry framework.

Contribution

It derives a Ginsparg-Wilson-like relation for parity in regularized lattice Chern-Simons theory, establishing a novel symmetry transformation.

Findings

Derived a Ginsparg-Wilson-like relation for parity

Constructed generalized parity transformations that preserve odd behavior

Applicable to regularized lattice Chern-Simons models

Abstract

Regularization modifies the (odd) behaviour of the Abelian Chern-Simons action under parity. This effect happens for any sensible regularization; in particular, on the lattice. However, as in the chiral symmetry case, there exist generalized parity transformations such that the regularized theory is odd, and the corresponding operator verifies a Ginsparg-Wilson like relation. We present a derivation of such a relation and of the corresponding symmetry transformations.