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Title:
Center symmetry, neutral bions, and (a tiny little bit of) resurgence theory
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Abstract:
Using the twisted partition function on R3×S1, we argue that the deconfinement phase transition in pure Yang-Mills theory for all simple gauge groups is continuously connected to a quantum phase transition that can be studied in a controlled way. We explicitly consider two classes of theories, gauge theories with a center symmetry, such as SU(Nc) gauge theory for arbitrary Nc, and theories without a center symmetry, such as G2 gauge theory. The mechanism governing the phase transition is universal and valid for all simple groups. The perturbative one-loop potential as well as monopole-instantons generate attraction among the eigenvalues of the Wilson line. This is counter-acted by neutral bions — topological excitations which generate eigenvalue repulsion for all simple groups. The transition is driven by the competition between these three effects. We study the transition in more detail for the gauge groups SU(Nc), Nc>2, and G2. In the case of G2, there is no change of symmetry, but the expectation value of the Wilson line exhibits a discontinuity. We also examine the effect of the θ-angle on the phase transition and critical temperature Tc(θ). The critical temperature is a multi-branched function, which has a minimum at θ=π as a result of topological intereference.
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