Two-flavor adjoint QCD

TL;DR

This paper analyzes a four-dimensional $SU(2)$ Yang-Mills theory with two adjoint Weyl fermions, showing that its symmetry and massless spectrum remain consistent from small to large circle sizes, suggesting no phase transition occurs.

Contribution

It demonstrates that the symmetry realization and massless spectrum in two-flavor adjoint QCD are preserved from weak-coupling small circle to strong-coupling large circle, indicating potential absence of phase transitions.

Findings

Symmetry and spectrum match between small and large circle limits.

All anomaly matching conditions are satisfied by the same massless spectrum.

The theory may not undergo phase transitions between different size regimes.

Abstract

We study four dimensional $SU(2)$ Yang-Mills theory with two massless adjoint Weyl fermions. When compactified on a spatial circle of size $L$ much smaller than the strong-coupling scale, this theory can be solved by weak-coupling nonperturbative semiclassical methods. We study the possible realizations of symmetries in the $\mathbb R^4$ limit and find that all continuous and discrete $0$-form and $1$-form 't Hooft anomaly matching conditions are saturated by a symmetry realization and massless spectrum identical to that found in the small-$L$ limit, with only a single massless flavor-doublet fermion in the infrared. This observation raises the possibility that the class of theories which undergo no phase transition between the analytically-solvable small-size circle and strongly-coupled infinite-size circle is larger than previously thought, and offers new challenges for lattice studies.