Abstract
We study the phase structure of N=1 supersymmetric Yang-Mills theory on R^3XS^1, with massive gauginos, periodic around the S^1, with Sp(2N) (N>=2), Spin(N) (N>=5), G_2, F_4, E_6, E_7, E_8 gauge groups. As the gaugino mass m is increased, with S^1 size and strong coupling scale fixed, we find a first-order phase transition both for theories with and without a center. This semiclassically calculable transition is driven, as in SU(N) and G_2, arxiv.org/abs/1205.0290 and arxiv.org/abs/1212.1238, by a competition between monopole-instantons and exotic topological "molecules"---"neutral" or "magnetic" bions. We compute the trace of the Polyakov loop and its two-point correlator near the transition. We find a behavior similar to the one observed near the thermal deconfinement transition in the corresponding pure Yang-Mills (YM) theory in lattice studies (whenever available). Our results lend further support to the conjectured continuity, as a function of m, between the quantum phase transition studied here and the thermal deconfinement transition in YM theory. We also study the theta-angle dependence of the transition, elaborate on the importance of the quantum-corrected moduli-space metric at large N, and offer comments for the future.
Highlights
The problems of confinement, deconfinement, and, more generally, the phases of nonabelian four-dimensional Yang-Mills theories remain among the most difficult issues in quantum field theory
We study the phase structure of N = 1 supersymmetric Yang-Mills theory on R3 × S1, with massive gauginos, periodic around the S1, with Sp(2N ) (N ≥ 2), Spin(N ) (N ≥ 5), G2, F4, E6, E7, E8 gauge groups
1 supersymmetric counterpart (SYM) with a supersymmetry breaking mass m for the gaugino — the Weyl fermion in the adjoint representation which is the superpartner of the gluon in the massless limit
Summary
The problems of confinement, deconfinement, and, more generally, the phases of nonabelian four-dimensional Yang-Mills theories remain among the most difficult issues in quantum field theory. Upon compactification of thermal Yang-Mills theory on S3 × S1β, using the size of S3 (smaller than Λ−1) as a control parameter allowing perturbative calculations, the authors of [12] showed that in the infinite-N limit there is a sharp phase transition associated with deconfinement, and occurring in the weakly-coupled regime; as this is a small volume system, infinite-N is necessary to have a phase transition. Another situation where analytic calculability is sometimes possible is to consider thermal YM, “deformed” or with adjoint fermions, partially compactified on R2 × S1L × S1β, using L Λ−1 as a control parameter (further in this paper we will use L = 2πR)..
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