Spatial volume dependence for 2+1 dimensional SU(N) Yang-Mills theory

Abstract

We study the 2+1 dimensional SU(N) Yang-Mills theory on a finite two-torus with twisted boundary conditions. Our goal is to study the interplay between the rank of the group N, the length of the torus L and the Z_N magnetic flux. After presenting the classical and quantum formalism, we analyze the spectrum of the theory using perturbation theory to one-loop and using Monte Carlo techniques on the lattice. In perturbation theory, results to all orders depend on the combination x=λNL and an angle defined in terms of the magnetic flux (λ is 't Hooft coupling). Thus, fixing the angle, the system exhibits a form of volume independence (NL dependence). The numerical results interpolate between our perturbative calculations and the confinement regime. They are consistent with x-scaling and provide interesting information about the k-string spectrum and effective string theories. The occurrence of tachyonic instabilities is also analysed. They seem to be avoidable in the large N limit with a suitable scaling of the magnetic flux.

62 pages, 7 figures

References in corpus (8)

• SU(N) gauge theories at large N
• Closed flux tubes and their string description in D=2+1 SU(N) gauge theories
• Seiberg-Witten and "Polyakov-like" magnetic bion confinements are continuously connected
• The string tension from smeared Wilson loops at large N
• The closed string spectrum of SU(N) gauge theories in 2+1 dimensions
• The Hamiltonian Approach to Yang-Mills (2+1): An Expansion Scheme and Corrections to String Tension
• k-String Tension from Eguchi-Kawai Reduction
• Phases of three dimensional large N QCD on a continuum torus

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• Testing volume independence of large N gauge theories on the lattice