Two-dimensional gauge theories of the symmetric group S(n) and branched n-coverings of Riemann surfaces in the large-n limit

Details Two-dimensional gauge theories of the symmetric group S(n) and branched n-coverings of Riemann surfaces in the large-n limit Two-dimensional gauge theories of the symmetric group S(n) and branched n-coverings of Riemann surfaces in the large-n limit

2002-01-23

arxiv.org/abs/hep-th/0201181v1

Nucl.Phys.Proc.Suppl. 108 (2002) 79-83

Physics

High Energy Physics

High Energy Physics - Theory

Talk presented at the "Light-cone physics: particles and strings", Trento, Italy, September 2001

Scientific paper

10.1016/S0920-5632(02)01308-7

Branched n-coverings of Riemann surfaces are described by a 2d lattice gauge theory of the symmetric group S(n) defined on a cell discretization of the surface. We study the theory in the large-n limit, and we find a rich phase diagram with first and second order transition lines. The various phases are characterized by different connectivity properties of the covering surface. We point out some interesting connections with the theory of random walks on group manifolds and with random graph theory.

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