A new large N phase transition in YM2

A. Apolloni, S. Arianos, A. D'Adda
2006 Nuclear Physics B  
Inspired by the interpretation of two dimensional Yang-Mills theory on a cylinder as a random walk on the gauge group, we point out the existence of a large N transition which is the gauge theory analogue of the cutoff transition in random walks. The transition occurs in the strong coupling region, with the 't Hooft coupling scaling as alpha*log(N), at a critical value of alpha (alpha = 4 on the sphere). The two phases below and above the transition are studied in detail. The effective number
more » ... degrees of freedom and the free energy are found to be proportional to N^(2-alpha/2) below the transition and to vanish altogether above it. The expectation value of a Wilson loop is calculated to the leading order and found to coincide in both phases with the strong coupling value.
doi:10.1016/j.nuclphysb.2006.03.017 fatcat:cebnchutubalxl2c23ayrec25y