Large-N volume reduction of lattice QCD with adjoint Wilson fermions at weak-coupling

Abstract

We study the large-N volume reduction of QCD with adjoint quarks regularized on the lattice. Specifically, we use Wilson fermions, and while our d-dimensional lattice has (d-1) infinite dimensions, the remaining direction is reduced to a point. We perform a weak-coupling one-loop calculation of the free energy as a function of the holonomy in the reduced direction, and map the regimes in the bare lattice parameter space where the holonomy averages to zero and a Z_N-center symmetric configuration is the ground state. For d=4 and N_f=1/2,1 and 2 Dirac flavors we see that the center symmetry is intact in a generous regime of the phase diagram that includes the chiral point. Thus we see that large-N volume independence of lattice QCD with adjoint Wilson quarks works at weak coupling. Interestingly, we find that this is true even if the quark mass is quite large, and this opens a path to study the volume reduced large-N pure gauge theory. Finally, we analyze in detail the UV sensitivity of the one-loop potential and show that treating the reduced theory as a (d-1)-dimensional effective field theory requires the introduction of certain relevant operators that are a subset of those suggested by Unsal and Yaffe to stabilize the center symmetry. This means that different regularizations of the volume-reduced theory can be compared only if one includes these terms in the action.

arXiv comment37 pages, 12 figures

References in corpus (12)

• Electroweak symmetry breaking from dimensional deconstruction
• (De)Constructing Dimensions
• A New Expansion for Nucleon-Nucleon Interactions
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Space-Time Structures from IIB Matrix Model
• Volume independence in large Nc QCD-like gauge theories
• Exact Results in Non-Supersymmetric Large N Orientifold Field Theories
• Tuning for Three-flavors of Anisotropic Clover Fermions with Stout-link Smearing
• Effective Theory of Wilson Lines and Deconfinement
• Does the crossover from perturbative to nonperturbative physics in QCD become a phase transition at infinite N ?
• Breakdown of large-N quenched reduction in SU(N) lattice gauge theories
• Is there an Aoki phase in quenched QCD?

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• Lattice study of two-dimensional N=(2,2) super Yang-Mills at large-N
• Large-N reduction in QCD-like theories with massive adjoint fermions
• Non-perturbative volume-reduction of large-N QCD with adjoint fermions
• Large N Volume Independence and an Emergent Fermionic Symmetry
• Finite Volume Phases of Large N Gauge Theories with Massive Adjoint Fermions
• The large N limit of four dimensional Yang-Mills field coupled to adjoint fermions on a single site lattice
• Large-N reduction of SU(N) Yang-Mills theory with massive adjoint overlap fermions
• Large-N reduced models of supersymmetric quiver, Chern-Simons gauge theories and ABJM
• Realization of Center Symmetry in Two Adjoint Flavor Large-N Yang-Mills
• Can fermions save large N dimensional reduction?
• k-String Tension from Eguchi-Kawai Reduction
• A PNJL Model for Adjoint Fermions with Periodic Boundary Conditions
• Bose-Fermi Degeneracies in Large $N$ Adjoint QCD
• Phase structure and Hosotani mechanism in gauge theories with compact dimensions revisited
• Comments on large-N volume independence
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• Weak-coupling analysis of the single-site large-N gauge theory coupled to adjoint fermions
• Four-dimensional N=1 super Yang-Mills from matrix model
• Numerical computation of the beta function of large N SU(N) gauge theory coupled to an adjoint Dirac fermion
• Partial breakdown of center symmetry in large-N QCD with adjoint Wilson fermions
• 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
• Eguchi-Kawai reduction with one flavor of adjoint Moebius fermion