Light Adjoint Quarks in the Instanton-Dyon Liquid Model IV

Abstract

We discuss the instanton-dyon liquid model with $N_f$ Majorana quark flavors in the adjoint representation of color $S{U}_c(2)$ at finite temperature. We briefly recall the index theorem on $S^1\times R^3$ for twisted adjoint fermions in a BPS dyon background of arbitrary holonomy, and use the ADHM construction to explicit the adjoint anti-periodic zero modes. We use these results to derive the partition function of an interacting instanton-dyon ensemble with $N_f$ light and anti-periodic adjoint quarks. We develop the model in details by mapping the theory on a 3-dimensional quantum effective theory with adjoint quarks with manifest $SU(N_f)\times Z_{4N_f}$ 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 $N_f=1$. For a sufficiently dense liquid, we find that the ground state is center symmetric and breaks spontaneously flavor symmetry through $SU(N_f)\times Z_{4N_f}\to O(N_f)$. As the liquid dilutes with increasing temperature, center symmetry and chiral symmetry are restored. We present numerical and analytical estimates for the transition temperatures.

22 pages, 6 figures

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Cited by in corpus (8)

• The Myriad Uses of Instantons
• The Instanton-Dyon Liquid Model V: Twisted Light Quarks
• The Instanton-Dyon Liquid Model III: Finite Chemical Potential
• Lectures on nonperturbative QCD ( Nonperturbative Topological Phenomena in QCD and Related Theories)
• Dense Instanton-Dyon Liquid Model: Diagrammatics
• D-instantons in Real Time Dynamics
• Hadronic Correlation Functions in the Random Instanton-dyon Ensemble
• Holographic spectroscopy of fermion with instantons