Gauge theories of the symmetric group S_n in the large n limit
Alessandro D`Adda
Abstract
We study the two dimensional gauge theory of the symmetric group S_n describing the statistic of branched n-coverings of Riemann surfaces. On the sphere a non trivial phase structure emerges, with various phases corresponding to different connectivity properties of the covering surface. We show that a gauge theory on a two dimensional surface of genus zero is equivalent to a random walk on the gauge group manifold\: in the case of S_n one of the phase transitions we find can be interpreted as a cutoff phenomenon on the corresponding random walk. A new phase transition corresponding to a cutoff phenomenon is also found in two dimensional Yang-Mills theory, if the coupling constant is scaled with N with an extra Log N, compared to the standard `t Hooft scaling. A connection with the theory of phase transitions in random graphs is also pointed out.
Elenco dei partecipanti al convegno di Bari.