Light adjoint quarks in the instanton-dyon liquid model. IV.

We discuss the instanton-dyon liquid model with Nf Majorana quark flavors in the adjoint representation of color SUc(2) at finite temperature. We briefly recall the index theorem on S1×R3 for twisted adjoint fermions in a Bogomolny-Prasad-Sommerfeld (BPS) dyon background of arbitrary holonomy and use the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction to derive the adjoint antiperiodic zero modes. We use these results to derive the partition function of an interacting instanton-dyon ensemble with Nf light and antiperiodic adjoint quarks. We develop the model in details by mapping the theory on a three-dimensional quantum effective theory with adjoint quarks with manifest SU(Nf)×Z4Nf symmetry. Using a mean-field analysis at weak coupling and strong screening, we show that center symmetry requires the spontaneous breaking of chiral symmetry, which is shown to only take place for Nf=1. For a sufficiently dense liquid, we find that the ground state is center symmetric and breaks spontaneously flavor symmetry through SU(Nf)×Z4Nf→O(Nf). As the liquid dilutes with increasing temperature, center symmetry and chiral symmetry are restored. We present numerical and analytical estimates for the transition temperatures.