Induced Polyakov supergravity on Riemann surfaces of higher genus

TL;DR

This paper derives an effective action for N=1 2D-induced supergravity on higher genus super Riemann surfaces, introducing new super integration techniques and exploring the relationship between symmetries and holomorphic structures.

Contribution

It presents a novel formulation of super integration and residue calculus on super Riemann surfaces, leading to a well-defined supergravity action free of singularities.

Findings

Effective supergravity action on higher genus surfaces derived

New super integration theory including super Stokes theorem developed

Connection between diffeomorphism symmetry and holomorphic properties established

Abstract

An effective action is obtained for the $N=1$, $2D-$induced supergravity on a compact super Riemann surface (without boundary) $\hat\Sigma$ of genus $g>1$, as the general solution of the corresponding superconformal Ward identity. This is accomplished by defining a new super integration theory on $\hat\Sigma$ which includes a new formulation of the super Stokes theorem and residue calculus in the superfield formalism. Another crucial ingredient is the notion of polydromic fields. The resulting action is shown to be well-defined and free of singularities on $\sig$. As a by-product, we point out a morphism between the diffeomorphism symmetry and holomorphic properties.