The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

TL;DR

This paper explores the non-perturbative dynamics of four-dimensional gauge theories with adjoint fermions using circle compactification, revealing new phenomena like gauge holonomy-induced Higgsing, monopole-instantons, bions, and their relation to resurgence and renormalons.

Contribution

It introduces a comprehensive semi-classical framework for gauge theories, connecting monopole effects, bions, and resurgence theory to understand non-perturbative phenomena.

Findings

Gauge holonomy induces Higgsing in all gauge groups.

Identification of magnetic and neutral bions affecting gauge dynamics.

Prediction of Borel plane singularities related to bions and renormalons.

Abstract

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are "magnetic bions" which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are "neutral bions" which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics - which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription - to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion--anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Ecalle's resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.