Gauge theory geography: charting a path between semiclassical islands

We study two semiclassical limits of SU(2) Yang-Mills theory on a spatial torus with a 't Hooft twist: the "femtouniverse," where all T-3 directions are small, and deformed Yang-Mills theory on T-2 x S-1, with small S-1 and large or infinite T-2. 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 theta-dependent vacuum structure of these theories. We then calculate the one-loop potential for the S-1-holonomy in the presence of twists on T-2. We use it to study the quantum stability of the semiclassical ground states in gauge theories with massive or massless adjoint fermions on spatial T-2 x S-1, with a twist in the T-2. The results point towards some interesting features worthy of further study.