Gauge theory geography: charting a path between semiclassical islands

Abstract

Abstract We study two semiclassical limits of SU(2) Yang-Mills theory on a spatial torus with a ’t Hooft twist: the “femtouniverse,” where all 𝕋3 directions are small, and deformed Yang-Mills theory on 𝕋2 × 𝕊1, with small 𝕊1 and large or infinite 𝕋2. Carefully defining the symmetries, we show that the classical ground states, while different, have the same transformation properties under the 1-form center symmetry and parity. We argue that this is behind the identical multi-branch θ-dependent vacuum structure of these theories. We then calculate the one-loop potential for the 𝕊1-holonomy in the presence of twists on 𝕋2. We use it to study the quantum stability of the semiclassical ground states in gauge theories with massive or massless adjoint fermions on spatial 𝕋2 × 𝕊1, with a twist in the 𝕋2. The results point towards some interesting features worthy of further study.