Torsion constraints of (2,0) supergravity and line integrals on N=2 super Riemann surfaces.

Abstract

We interpret the torsion constraints of (2,0) supergravity in two dimensions from the viewpoint of $N=2$ super Riemann surfaces. However, because ${{T}_{\ifmmode\pm\else\textpm\fi{}\overline{z}}}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\ne}0$, these torsion constraints are not appropriate for defining the line integral on an $N=2$ super Riemann surface of any genus. In order to cure these difficulties, we introduce a U(1) connection and then obtain a new set of torsion constraints. Finally, we define the line integral on $N=2$ super Riemann surfaces by using an analogue of the sheaf-theoretic prescription of the line integral on a Riemann surface.