Partial breakdown of center symmetry in large-N QCD with adjoint Wilson fermions

Abstract

We study the one-loop potential of large-N QCD with adjoint Dirac fermions. Space-time is a discretization of R^3 x S^1 where the compact direction consists of a single lattice site. We use Wilson fermions with different values of the quark mass m and set the lattice spacings in the compact and non-compact directions to be a_t and a_s respectively. Extending the results of JHEP 0906:091,2009, we prove that if the ratio xi = a_s/a_t obeys 0<xi<2, then the minimum of the one-loop lattice potential for one or more Dirac flavors is Z_N symmetric at the chiral point. For xi=0 our formulas reduce to those obtained in a continuum regularization of the R^3, and our proof holds in that case as well. As we increase m from zero, we find a cascade of transitions where Z_N breaks to Z_K. For very small masses, K ~ 1/(a_t m) >> 1, while for large masses K ~ O(1). Despite certain UV sensitivities of the lattice one-loop potential, this phase structure is similar to the one obtained in the continuum works of Kovtun-Unsal-Yaffe, Myers-Ogilvie, and Hollowood-Myers. We explain the physical origin of the cascade of transitions and its relation to the embedding of space-time into color space.

22 pages, 3 figures. V2: one typo corrected. published version

References in corpus (7)

• Volume independence in large Nc QCD-like gauge theories
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Finite size phase transitions in QCD with adjoint fermions
• Phase diagrams of SU(N) gauge theories with fermions in various representations
• Finite Volume Phases of Large N Gauge Theories with Massive Adjoint Fermions
• Large-N volume reduction of lattice QCD with adjoint Wilson fermions at weak-coupling
• Can fermions save large N dimensional reduction?

Cited by in corpus (8)

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• Large-N reduction in QCD with two adjoint Dirac fermions
• Realization of Center Symmetry in Two Adjoint Flavor Large-N Yang-Mills
• k-String Tension from Eguchi-Kawai Reduction
• Large N and Bosonization in Three Dimensions
• A Scaling Relation, $Z_m$-type Deconfinement Phases and Imaginary Chemical Potentials in Finite Temperature Large-$N$ Gauge Theories