Gauge theory geography: charting a path between semiclassical islands

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 \U0001d54b3 directions are small, and deformed Yang-Mills theory on \U0001d54b2 × \U0001d54a1, with small \U0001d54a1 and large or infinite \U0001d54b2. 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 \U0001d54a1-holonomy in the presence of twists on \U0001d54b2. We use it to study the quantum stability of the semiclassical ground states in gauge theories with massive or massless adjoint fermions on spatial \U0001d54b2 × \U0001d54a1, with a twist in the \U0001d54b2. The results point towards some interesting features worthy of further study.