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

We interpret the torsion constraints of (2,0) supergravity in two dimensions from the viewpoint of N=2 super Riemann surfaces. However, because T±barz±≠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