Gauge theory geography: charting a path between semiclassical islands
Erich Poppitz, F. David Wandler
Abstract
A bstract 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 × 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 θ -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 × 𝕊 1 , with a twist in the 𝕋 2 . The results point towards some interesting features worthy of further study.