Branched coverings and Yang-Mills theories in two dimensions.
Paolo Provero


Abstract
We discuss the relationship between two dimensional Yang-Mills theories and branched coverings of Riemann surfaces. First we review the equivalence between the theory of branched coverings and the 2D gauge theory of the symmetric group. Then we show how one can consistently introduce a U(1) gauge theory living on the world sheet of such branched coverings. The resulting theory is shown to be equivalent to a certain generalized U(N) Yang-Mills theory quantized in the unitary gauge.

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