$\theta$-dependence and center symmetry in Yang-Mills theories

Understand

We investigate the relation between the realization of center symmetry and the dependence on the topological parameter $\theta$ in $SU(N)$ Yang-Mills theories, exploiting trace deformations as a tool to regulate center symmetry breaking in a theory with a small compactified direction.

• We consider, in particular, $SU(4)$ gauge theory, which admits two possible independent deformations, and study, as a first step, its phase diagram in the deformation plane for two values of the inverse compactified radius going up to $L^{-1} \sim 500$ MeV, comparing the predictions of the effective 1-loop potential of the Polyakov loop with lattice results.
• The $\theta$-dependence of the various phases is then addressed, up to the fourth order in $\theta$, by numerical simulations: results are found to coincide, within statistical errors, with those of the standard confined phase iff center symmetry is completely restored and independently of the particular way this happens, i.e.
• either by local suppression of the Polyakov loop traces or by long range disorder.