2009/04/30 by Paulo F. Bedaque, Michael I. Buchoff, Aleksey Cherman +1 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Dimensional reduction #Fermion #Gauge symmetry #Gauge theory #Geometry #Homogeneous space #Mathematical physics #Mathematics #Orbifold #Particle physics theoretical and experimental studies #Physics #Projection (relational algebra) #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Reduction (mathematics) #Supersymmetric gauge theory #Theoretical physics #hep-lat #hep-ph #hep-th
paper · pdf · doi:10.1088/1126-6708/2009/10/070
published as JHEP 0910:070,2009 · 24 pages, 3 figures. Added a postscript to discuss issues raised in arXiv:0905.2406
arxiv created 2009/08/21 · openalex publication_date 2009/10/26 · arxiv updated 2010/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.