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We study the phase diagrams of $\Nc= \infty$ vector-like, asymptotically freegauge theories as a function of volume, on $S^3\times S^1$. The theories ofinterest are the ones with fermions in two index representations [adjoint,(anti)symmetric, and bifundamental abbreviated as QCD(adj), QCD(AS/S) andQCD(BF)], and are interrelated via orbifold or orientifold projections. Thephase diagrams reveal interesting phenomena such as disentangled realizationsof chiral and center symmetry, confinement without chiral symmetry breaking,zero temperature chiral transitions, and in some cases, exotic phases whichspontaneously break the discrete symmetries such as C, P, T as well as CPT. Ina regime where the theories are perturbative, the deconfinement temperature inSYM, and QCD(AS/S/BF) coincide. The thermal phase diagrams of thermal orbifoldQCD(BF), orientifold QCD(AS/S), and $\N=1$ SYM coincide, provided chargeconjugation symmetry for QCD(AS/S) and $\Z_2$ interchange symmetry of theQCD(BF) are not broken in the phase continously connected to $\R^4$ limit. Whenthe $S^1$ 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 spinstructure of fermions along the $S^1$ circle is naturally explained in terms ofthe necessary and sufficient symmetry realization conditions which determinethe validity of the nonperturbative orbifold orientifold equivalence.Comment: 60 pages, 6 figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Phases of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mo>∞</mml:mo></mml:math>QCD-like gauge theories on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>S</mml:mi><mml:mn>3</mml:mn></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mi>S</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math>and nonperturbative orbifold-orientifold equivalences

Phases ofN=∞QCD-like gauge theories onS3×S1and nonperturbative orbifold-orientifold equivalences