N-Point Functions of 2d Yang–Mills Theories on Riemann Surfaces

Abstract

Using the simple path integral method we calculate the n-point functions of field strength of Yang–Mills theories on arbitrary two-dimensional Riemann surfaces. In U(1) case we show that the correlators consist of two parts, a free and an x-independent part. In the case of non-Abelian semisimple compact gauge groups we find the nongauge-invariant correlators in Schwinger–Fock gauge and show that it is also divided to a free and an almost x-independent part. We also find the gauge-invariant Green functions and show that they correspond to a free field theory.