Conformality or confinement: (IR)relevance of topological excitations

TL;DR

This paper investigates the transition from conformality to confinement in non-supersymmetric Yang-Mills theories by analyzing the behavior of the mass gap on R*3xS*1, providing new insights into the conformal window and semi-classical solvability.

Contribution

It introduces a non-perturbative method to study the mass gap on R*3xS*1 for various fermion representations, offering estimates of the conformal window and identifying conditions for semi-classical solvability.

Findings

Mass gap increases with radius for small Nf due to monopoles and bions.

Mass gap decreases with radius for large Nf, indicating different IR behavior.

First examples of semi-classically solvable Yang-Mills theories at any S*1 size.

Abstract

We study aspects of the conformality to confinement transition for non-supersymmetric Yang-Mills theories with fermions in arbitrary chiral or vectorlike representations. We use the presence or absence of mass gap for gauge fluctuations as an identifier of the infrared behavior. Present-day understanding does not allow the mass gap for gauge fluctuations to be computed on R*4. However, recent progress allows its non-perturbative computation on R*3xS*1 by using either the twisted partition function or deformation theory, for a range of S*1 sizes depending on the theory. For small number of fermions, Nf, we show that the mass gap increases with increasing radius, due to the non-dilution of monopoles and bions, the topological excitations relevant for confinement on R*3xS*1. For sufficiently large Nf, we show that the mass gap decreases with increasing radius. In a class of theories, we claim that the decompactification limit can be taken while remaining within the region of validity of semi-classical techniques, giving the first examples of semiclassically solvable Yang-Mills theories at any size S*1. For general non-supersymmetric vectorlike or chiral theories, we conjecture that the change in the behavior of the mass gap on R*3xS*1 as a function of the radius occurs near the lower boundary of the conformal window and give non-perturbative estimates of its value. For vectorlike theories, we compare our estimates of the conformal window with existing lattice results, truncations of the Schwinger-Dyson equations, NSVZ beta function-inspired estimates, and degree of freedom counting criteria. For multi-generation chiral gauge theories, to the best of our knowledge, our estimates of the conformal window are the only known ones.