  We study two semiclassical limits of $SU(2)$ Yang-Mills theory on a spatial
torus with a 't Hooft twist: the ``femtouniverse,'' where all $\mathbb{T}^3$
directions are small, and deformed Yang-Mills theory on $\mathbb{T}^2 \times
\mathbb{S}^1$, with small $\mathbb{S}^1$ and large or infinite $\mathbb{T}^2$.
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 $\mathbb{S}^1$-holonomy in the
presence of twists on $\mathbb{T}^2$. We use it to study the quantum stability
of the semiclassical ground states in gauge theories with massive or massless
adjoint fermions on spatial $\mathbb{T}^2 \times \mathbb{S}^1$, with a twist in
the $\mathbb{T}^2$. The results point towards some interesting features worthy
of further study.
