Arbitrary parameters in implicit regularization and democracy within perturbative description of 2-dimensional gravitational anomalies

TL;DR

This paper demonstrates how the Implicit Regularization Technique can analyze quantum symmetry breaking in 2D gravitational anomalies, revealing the interplay of arbitrary parameters and Ward identities without relying on specific regularization schemes.

Contribution

It introduces a regularization-independent method to study quantum anomalies and symmetry violations in 2D gravity, clarifying the role of arbitrary parameters in Ward identities.

Findings

The axial part of the Einstein Ward identity is always violated.

Pure tensor part of Einstein Ward identity can be preserved or violated independently.

The method allows algebraic analysis of symmetry breaking without fixing regularization parameters.

Abstract

We show that the Implicit Regularization Technique is useful to display quantum symmetry breaking in a complete regularization independent fashion. Arbitrary parameters are expressed by finite differences between integrals of the same superficial degree of divergence whose value is fixed on physical grounds (symmetry requirements or phenomenology). We study Weyl fermions on a classical gravitational background in two dimensions and show that, assuming Lorentz symmetry, the Weyl and Einstein Ward identities reduce to a set of algebraic equations for the arbitrary parameters which allows us to study the Ward identities on equal footing. We conclude in a renormalization independent way that the axial part of the Einstein Ward identity is always violated. Moreover whereas we can preserve the pure tensor part of the Einstein Ward identity at the expense of violating the Weyl Ward identities we may as well violate the former and preserve the latter.