Deformed dimensional regularization for odd (and even) dimensional theories

TL;DR

This paper introduces a novel deformation of dimensional regularization tailored for odd and even dimensional theories, avoiding inconsistencies and improving practical computations especially in three-dimensional gauge theories.

Contribution

A new regularization method that preserves gauge invariance and Lorentz invariance in the physical sector, specifically designed for odd-dimensional theories where standard techniques fail.

Findings

Effective in three-dimensional Chern-Simons gauge theories

Universal, local, and gauge-invariant regularization

Simplifies computations by automatically dropping evanescent operators

Abstract

I formulate a deformation of the dimensional-regularization technique that is useful for theories where the common dimensional regularization does not apply. The Dirac algebra is not dimensionally continued, to avoid inconsistencies with the trace of an odd product of gamma matrices in odd dimensions. The regularization is completed with an evanescent higher-derivative deformation, which proves to be efficient in practical computations. This technique is particularly convenient in three dimensions for Chern-Simons gauge fields, two-component fermions and four-fermion models in the large N limit, eventually coupled with quantum gravity. Differently from even dimensions, in odd dimensions it is not always possible to have propagators with fully Lorentz invariant denominators. The main features of the deformed technique are illustrated in a set of sample calculations. The regularization is universal, local, manifestly gauge-invariant and Lorentz invariant in the physical sector of spacetime. In flat space power-like divergences are set to zero by default. Infinitely many evanescent operators are automatically dropped.