Abstract
Using the Krichever-Novikov bases and the operator product expansions, the author constructs the N=2 superconformal algebra on a genus-g Riemann surface and the BRST charge corresponding to the superconformal algebra. He also checks the nilpotency of the BRST charge, and obtains the critical dimension of spacetime as D=2 for the N=2 superconformal theory on the higher-genus Riemann surface.
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