IR properties of Yang-Mills theories from the Batalin-Vilkovisky formalism

TL;DR

This paper reviews the Batalin-Vilkovisky formalism's application to Yang-Mills theories, emphasizing its role in deriving identities that connect Green's functions and aid in understanding infrared dynamics from lattice data.

Contribution

It demonstrates how the Batalin-Vilkovisky formalism can be used to derive identities relevant for analyzing IR properties of Yang-Mills theories in the continuum and lattice frameworks.

Findings

Derivation of identities relating background and quantum Green's functions.

Application of formalism to extract effective charge from lattice data.

Enhanced understanding of IR dynamics in Yang-Mills theories.

Abstract

The powerful quantization formalism of Batalin and Vilkovisky streamlines the derivation of the complete set of (non-linear) identities arising from the local BRST symmetry of Yang-Mills theories. When applied in the Background Field Method type of gauges, it also gives rise to identities which relate Green's functions involving background fields to Green's functions involving quantum fields. All these identities lie at the core of the recent progress in understanding from the continuum formulation the IR dynamics emerging from lattice simulations. In this talk, we will first review the Batalin-Vilkovisky formalism and then apply it to the problem of extracting the effective charge from the available lattice data.