2004/07/07 by Robert G. Leigh, Leigh, Robert G., Djordje Minic +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0407051
18 pages, LaTeX; discussion of QCD string expanded and references added
arxiv created 2004/08/24 · arxiv updated 2009/12/01
We study the large N (planar) limit of pure SU(N) 2+1 dimensional Yang-Mills theory (YM2+1) using a gauge-invariant matrix parameterization introduced by Karabali and Nair. This formulation crucially relies on the properties of local holomorphic gauge invariant collective fields in the Hamiltonian formulation of YM2+1. We show that the spectrum in the planar limit of this theory can be explicitly determined in the N=∞, low momentum (large 't Hooft coupling) limit, using the technology of the Eguchi-Kawai reduction and the existing knowledge concerning the one-matrix model. The dispersion relation describing the planar YM2+1 spectrum reads as ω(k) = √k2 + mn2, where n=1,2,... and mn = n mr, where mr denotes the renormalized mass, the bare mass m being determined by the planar 't Hooft coupling gYM2 N via m= \fracgYM2 N2 π. The planar, low momentum limit, also captures the expected short and long distance physics of YM2+1 and gives an interesting new picture of confinement. The computation of the spectrum is possible due to a reduction of the YM2+1 Hamiltonian for the large 't Hooft coupling to the \it singlet sector of an effective one matrix model. The crucial observation is that the correct vacuum (the large N master field), consistent with the area law and the existence of a mass gap, is described by an effective quadratic matrix model, in the large N, large 't Hooft coupling limit.