Can fermions save large N dimensional reduction?

Abstract

This paper explores whether Eguchi-Kawai reduction for gauge theories with adjoint fermions is valid. The Eguchi-Kawai reduction relates gauge theories in different numbers of dimensions in the large $N$ limit provided that certain conditions are met. In principle, this relation opens up the possibility of learning about the dynamics of 4D gauge theories through techniques only available in lower dimensions. Dimensional reduction can be understood as a special case of large $N$ equivalence between theories related by an orbifold projection. In this work, we focus on the simplest case of dimensional reduction, relating a 4D gauge theory to a 3D gauge theory via an orbifold projection. A necessary condition for the large N equivalence between the 4D and 3D theories to hold is that certain discrete symmetries in the two theories must not be broken spontaneously. In pure 4D Yang-Mills theory, these symmetries break spontaneously as the size of one of the spacetime dimensions shrinks. An analysis of the effect of adjoint fermions on the relevant symmetries of the 4D theory shows that the fermions help stabilize the symmetries. We consider the same problem from the point of view of the lower dimensional 3D theory and find that, surprisingly, adjoint fermions are not generally enough to stabilize the necessary symmetries of the 3D theory. In fact, a rich phase diagram arises, with a complicated pattern of symmetry breaking. We discuss the possible causes and consequences of this finding.

24 pages, 3 figures. Added a postscript to discuss issues raised in arXiv:0905.2406

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Cited by in corpus (21)

• SU(N) gauge theories at large N
• Finite size phase transitions in QCD with adjoint fermions
• 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
• 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 reduced models of supersymmetric quiver, Chern-Simons gauge theories and ABJM
• Realization of Center Symmetry in Two Adjoint Flavor Large-N Yang-Mills
• k-String Tension from Eguchi-Kawai Reduction
• Bose-Fermi Degeneracies in Large $N$ Adjoint QCD
• Comments on large-N volume independence
• 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
• 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
• Topics in Lattice QCD and Effective Field Theory
• Eguchi-Kawai model with dynamical adjoint fermions
• Volume independence of large-N QCD with adjoint fermions
• Continuum reduction in large N gauge theories