Background dependent cutoff for Wilson actions

TL;DR

This paper explores how background dependence affects Wilson actions within the exact renormalization group framework, highlighting the role of Ward identities and analyzing specific models like the Gaussian fixed point and large N limit.

Contribution

It provides a detailed analysis of background-dependent Wilson actions and their Ward identities in the ERG framework, with explicit examples and implications.

Findings

Background dependence influences Wilson actions and Ward identities.

The Ward identity for Wilson actions relates to that for the 1PI effective action.

Illustrated with Gaussian fixed point and large N linear sigma model.

Abstract

We study the application of the background field method in the framework of the exact renormalization group (ERG). By considering the case of a scalar field theory, we provide a detailed discussion of the properties satisfied by a background dependent Wilson action. We show how the Ward identity associated with background field shifts for the Wilson action is related to that for the 1PI Wilson action, or effective average action. Moreover, we discuss the ERG equations in the dimensionless framework and emphasize the role of the Ward identity in this setting. We give two examples: the Gaussian fixed point for the real scalar theory and the large $N$ limit of the linear sigma model.