1998/07/03 by P. H. Damgaard, Damgaard, P. H.
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9807026
LaTeX, 6 pages
arxiv created 1998/07/03 · arxiv updated 2009/11/30
Recent work on the spectrum of the Euclidean Dirac operator spectrum show that the exact microscopic spectral density can be computed in both random matrix theory, and directly from field theory. Exact relations to effective Lagrangians with additional quark species form the bridge between the two formulations. Taken together with explicit computations in the chGUE random matrix ensemble, a series of universality theorems are used to prove that the finite-volume QCD partition function coincides exactly with the universal double-microscopic limit of chUE random matrix partition functions. In the limit where Nf and Nc both go to infinity with the ratio Nf/Nc fixed, the relevant effective Lagrangian undergoes a third order phase transition of Gross-Witten type.