N=2 superconformal algebra, Ward identities and differential equations for correlators on super-Riemann surfaces.

Abstract

The $N=2$ superconformal algebra defined globally on higher-genus super-Riemann surfaces is obtained in terms of Krichever-Novikov bases. We derive the Ward identities of correlation functions on super-Riemann surfaces for $N=2$ superconformal field theories in the Krichever-Novikov approach from the superconformal transformation of $N=2$ primary fields. Finally, the partial differential equations satisfied by the correlators are given.