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

Abstract

Abstract:We study the phase diagrams of N = ∞ vector-like, asymptotically free gauge theories as a function of volume, on S 3 × 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 N = 1 SYM coincide, provided charge conjugation symmetry for QCD(AS/S) and Z 2 interchange symmetry of the QCD(BF) are not broken in the phase continously connected to 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 N = 1 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.

New Nonperturbative Methods in Quantum Field Theory: From Large-NOrbifold Equivalence to Bions and Resurgence

“…Assume equivalence is valid. Then, if either the parent or daughter theory has a global symmetry which protects an observable, then in the other theory (which does not possess the same global symmetry) the image observable behaves as if it is protected by the higher symmetry of the companion [15,16]. Why is this so?…”

“…We also mention that large-N equivalences also have useful applications to finite density QCD [22,23], and reveal a certain universality of the phase structure in different QCD-like theories [15,21].…”

“…In non-supersymmetric theories, its role has been understood only recently [15,[45][46][47]. It can be used to find the phases of a theory as a function of the spatial compactification radius (which now has no thermal interpretation).…”

“…This implies that the gluon condensate must vanish. As a result of equivalence, in non-supersymmetric QCD(AS) the gluon condensate must also be zero, at leading order in the 1/N expansion, scaling as [15]:…”

k-string tension from Eguchi-Kawai reduction

“…the finite temperature case), the theory is confining at an arbitrarily small radius and the condition for volume reduction is satisfied. Following their work several papers [5][6][7][8][9][10][11][12][13][14][15][16][17] supporting the validity of volume reduction for theories with adjoint fermions were published. This observation becomes particularly interesting when combined with…”