Exact renormalization group in Batalin--Vilkovisky theory

TL;DR

This paper develops a comprehensive formulation of the exact renormalization group within the Batalin-Vilkovisky framework, introducing supersymmetry in scale space and analyzing its implications for effective actions and flow equations.

Contribution

It extends BV RG theory by incorporating a supersymmetric structure in scale space, providing new insights into the flow of effective actions and their perturbative behavior.

Findings

BV RG supersymmetry constrains the RG equations to Polchinski's form

Constructed free models exhibiting BV RG flow and supersymmetry

Perturbative analysis of the deviation of interacting flow from free flow

Abstract

In this paper, inspired by the Costello's seminal work, we present a general formulation of exact renormalization group (RG) within the Batalin-Vilkovisky (BV) quantization scheme. In the spirit of effective field theory, the BV bracket and Laplacian structure as well as the BV effective action (EA) depend on an effective energy scale. The BV EA at a certain scale satisfies the BV quantum master equation at that scale. The RG flow of the EA is implemented by BV canonical maps intertwining the BV structures at different scales. Infinitesimally, this generates the BV exact renormalization group equation (RGE). We show that BV RG theory can be extended by augmenting the scale parameter space R to its shifted tangent bundle T[1]R. The extra odd direction in scale space allows for a BV RG supersymmetry that constrains the structure of the BV RGE bringing it to Polchinski's form. We investigate the implications of BV RG supersymmetry in perturbation theory. Finally, we illustrate our findings by constructing free models of BV RG flow and EA exhibiting RG supersymmetry in the degree -1 symplectic framework and studying the perturbation theory thereof. We find in particular that the odd partner of effective action describes perturbatively the deviation of the interacting RG flow from its free counterpart.