Branched coverings and interacting matrix strings in two dimensions Original Research Article

We construct the lattice gauge theory of the group GN, the semidirect product of the permutation group SN with U(1)N, on an arbitrary Riemann surface. This theory describes the branched coverings of a two-dimensional target surface by strings carrying a U(1) gauge field on the world-sheet. These are the nonsupersymmetric matrix strings that arise in the unitary gauge quantization of a generalized two-dimensional Yang–Mills theory. By classifying the irreducible representations of GN, we give the most general formulation of the lattice gauge theory of GN, which includes arbitrary branching points on the world-sheet and describes the splitting and joining of strings.