Monopole Condensation and Antisymmetric Tensor Fields: Compact QED and the Wilsonian RG Flow in Yang-Mills Theories

TL;DR

This paper presents a field-theoretic approach to monopole condensation in gauge theories using antisymmetric tensor fields, analyzing the Wilsonian RG flow and fixed points in Yang-Mills theories.

Contribution

It derives the monopole condensation action for 4d compact QED and explores the Wilsonian RG flow in Yang-Mills theories with tensor collective fields, identifying a fixed point related to monopole condensation.

Findings

Explicit derivation of the monopole condensation action for 4d compact QED.

Identification of a Ward identity as a fixed point of the Wilsonian RG flow.

Demonstration that monopole condensation corresponds to a specific RG fixed point.

Abstract

A field theoretic description of monopole condensation in strongly coupled gauge theories is given by actions involving antisymmetric tensors B_{\mu\nu} of rank 2. We rederive the corresponding action for 4d compact QED, summing explicitly over all possible monopole configurations. Its gauge symmetries and Ward identities are discussed. Then we consider the Wilsonian RGs for Yang-Mills theories in the presence of collective fields (again tensors B_{\mu\nu}) for the field strengths F_{\mu \nu} associated to the U(1) subgroups. We show that a ``vector-like'' Ward identity for the Wilsonian action involving B_{\mu\nu}, whose validity corresponds to monopole condensation, constitutes a fixed point of the Wilsonian RG flow.