BRST quantization ofN = 2, 3, and 4 superconformal theories on higher-genus Riemann surfaces

Complex contour integral techniques, developed in a previous paper for theN=0 and 1 superconformal theories on higher-genus Riemann surfaces, are applied to a Becchi-Rouet-Stora-Tyutin (BRST) quantization procedure of superconformal theories withN=2, 3, and 4 super-Krichever-Novikov (KN) constraint algebras on a genus-g Riemann surface. The BRST charges of the superconformai theories are constructed and the nilpotency of the BRST charges is checked. The critical spacetime dimension and the intercepts are found for theN=2 and 4 cases. Also calculated are the central charge and the intercept for theN=3 case.