Induced Chern-Simons-like action in Lorentz-violating massless QED

TL;DR

This paper investigates how Lorentz and CPT symmetry violations in extended massless QED can induce a well-defined, finite Chern-Simons-like term, supported by multiple regularization schemes and relating 3+1 and 2+1 dimensional theories.

Contribution

It demonstrates that the Chern-Simons-like term in extended massless QED can be consistently induced with a finite coefficient, bridging 3+1 and 2+1 dimensional frameworks.

Findings

The Chern-Simons-like term can be induced with a finite coefficient.

Multiple regularization schemes support the finiteness and well-defined nature of the term.

The work connects 3+1 dimensional extended QED to 2+1 dimensional massive QED.

Abstract

In the present work, we study different aspects of Lorentz and CPT symmetry violation in extended massless QED. By following the observation that the 2+1 dimensional Maxwell-Chern-Simons theory can be originated from the 3+1 dimensional Chern-Simons-like action, we also focus on the fermion sector to relate the 3+1 dimensional extended massless QED to 2+1 dimensional massive QED. We take advantage of this to state that the Chern-Simons-like action in extended massless QED can be induced with its coefficient being well defined and finite just as its 2+1 counterpart. We make use of three different regularization schemes by inducting the Chern-Simons-like in 3+1 dimensions to support this conjecture.