Phases of $\Nc= \infty$ QCD-like gauge theories on $S^3\times S^1$ and nonperturbative orbifold-orientifold equivalences

Abstract

We study the phase diagrams of $\Nc= \infty$ vector-like, asymptotically free gauge theories as a function of volume, on $S^3\times S^1$. The theories of interest are the ones with fermions in two index representations [adjoint, (anti)symmetric, and bifundamental abbreviated as QCD(adj), QCD(AS/S) and QCD(BF)], and are interrelated via orbifold or orientifold projections. The phase diagrams reveal interesting phenomena such as disentangled realizations of chiral and center symmetry, confinement without chiral symmetry breaking, zero temperature chiral transitions, and in some cases, exotic phases which spontaneously break the discrete symmetries such as C, P, T as well as CPT. In a regime where the theories are perturbative, the deconfinement temperature in SYM, and QCD(AS/S/BF) coincide. The thermal phase diagrams of thermal orbifold QCD(BF), orientifold QCD(AS/S), and $\mathbb{N}=1$ SYM coincide, provided charge conjugation symmetry for QCD(AS/S) and ${\mathbb{Z}}_2$ interchange symmetry of the QCD(BF) are not broken in the phase continously connected to ${\mathbb{R}}^4$ limit. When the $S^1$ circle is endowed with periodic boundary conditions, the (nonthermal) phase diagrams of orbifold and orientifold QCD are still the same, however, both theories possess chirally symmetric phases which are absent in $\None$ SYM. The match and mismatch of the phase diagrams depending on the spin structure of fermions along the $S^1$ circle is naturally explained in terms of the necessary and sufficient symmetry realization conditions which determine the validity of the nonperturbative orbifold orientifold equivalence.

60 pages, 6 figures

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Cited by in corpus (16)

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• Large-N reduction in QCD-like theories with massive adjoint fermions
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• IR Renormalons vs. Operator Product Expansion in Supersymmetric and Related Gauge Theories
• Finite Volume Phases of Large N Gauge Theories with Massive Adjoint Fermions
• Chiral gap effect in curved space
• Sign problem and phase quenching in finite-density QCD: models, holography, and lattice
• Explicit Non-Abelian Monopoles and Instantons in SU(N) Pure Yang-Mills Theory
• Planar Limit of Orientifold Field Theories and Emergent Center Symmetry
• Hedgehog black holes and the Polyakov loop at strong coupling
• Phases of Thermal N=2 Quiver Gauge Theories
• Some Theoretical Developments in SUSY
• Confinement, Screening and the Center on S^3 x S^1
• Thermal evolution of dark matter and gravitational-wave production in the early universe from a symplectic glueball model
• Flow of Hagedorn singularities and phase transitions in large $N$ gauge theories
• Theoretical Developments in SUSY