Strong to weak coupling transitions of SU(N) gauge theories in 2+1 dimensions

Abstract

We investigate strong-to-weak coupling transitions in D=2+1 SU(N->oo) gauge theories, by simulating lattice theories with a Wilson plaquette action. We find that there is a strong-to-weak coupling cross-over in the lattice theory that appears to become a third-order phase transition at N=oo, in a manner that is essentially identical to the Gross-Witten transition in the D=1+1 SU(oo) lattice gauge theory. There is also evidence for a second order transition at N=oo at approximately the same coupling, which is connected with centre monopoles (instantons) and so analogues to the first order bulk transition that occurs in D=3+1 lattice gauge theories for N>4. We show that as the lattice spacing is reduced, the N=oo gauge theory on a finite 3-torus suffers a sequence of (apparently) first-order ZN symmetry breaking transitions associated with each of the tori (ordered by size). We discuss how these transitions can be understood in terms of a sequence of deconfining transitions on ever-more dimensionally reduced gauge theories.We investigate whether the trace of the Wilson loop has a non-analyticity in the coupling at some critical area, but find no evidence for this although, just as in D=1+1,the eigenvalue density of a Wilson loop forms a gap at N=oo for a critical trace. The physical implications of this are unclear.The gap formation is a special case of a remarkable similarity between the eigenvalue spectra of Wilson loops in D=1+1 and D=2+1 (and indeed D=3+1): for the same value of the trace, the eigenvalue spectra are nearly identical.This holds for finite as well as infinite N; irrespective of the Wilson loop size in lattice units; and for Polyakov as well as Wilson loops.

arXiv comment44 pages, 28 figures. Extensive changes and clarifications with new results on non-analyticities and eigenvalue spectra of Wilson loops. This version to be submitted for publication

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• Computation of the string tension in four-dimensional Yang-Mills theory using large N reduction
• Phases of three dimensional large N QCD on a continuum torus
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• The Heisenberg XX spin chain and low-energy QCD
• Three dimensional finite temperature SU(3) gauge theory in the confined region and the string picture
• Finite-temperature phase transitions of third and higher order in gauge theories at large $N$
• Computation of the string tension in three dimensional Yang-Mills theory using large N reduction
• SO(2N) and SU(N) gauge theories in 2+1 dimensions
• Confining strings in three-dimensional gauge theories beyond the Nambu--Gotō approximation
• More about QCD on compact spaces
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• Topological order and the vacuum of Yang-Mills theories
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