Apparently non-invariant terms of nonlinear sigma models in lattice perturbation theory

TL;DR

This paper investigates the appearance of apparently non-invariant terms in lattice perturbation theory for nonlinear sigma models, demonstrating their regularization scheme independence and clarifying the role of the Jacobian.

Contribution

It provides a lattice regularization analysis confirming that ANTs are scheme-independent and clarifies the Jacobian's role in their generation.

Findings

ANTs appear in lattice perturbation theory at one-loop

The Jacobian does not significantly contribute to ANTs

ANTs are independent of the regularization scheme

Abstract

Apparently non-invariant terms (ANTs) which appear in loop diagrams for nonlinear sigma models (NLSs) are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to "pion" fields, we employ lattice regularization, in which everything (including the Jacobian) is well-defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the "pion" fields at one-loop and the Jacobian does not play an important role in generating ANTs.