Super-Chern-Simons Theory as Superstring Theory

TL;DR

This paper develops a geometric framework for computing superstring amplitudes involving supermanifolds, addressing longstanding difficulties in higher-genus calculations and connecting superstring theory with super-Chern-Simons theory.

Contribution

It introduces a systematic geometric approach to superstring amplitude computations and links supermanifold integration with topological string theory.

Findings

Established a translation between supermanifold theory and topological strings.

Constructed picture changing operators for superstring amplitude calculations.

Derived amplitude prescriptions from extended topological gravity coupling.

Abstract

Superstrings and topological strings with supermanifolds as target space play a central role in the recent developments in string theory. Nevertheless the rules for higher-genus computations are still unclear or guessed in analogy with bosonic and fermionic strings. Here we present a common geometrical setting to develop systematically the prescription for amplitude computations. The geometrical origin of these difficulties is the theory of integration of superforms. We provide a translation between the theory of supermanifolds and topological strings with supertarget space. We show how in this formulation one can naturally construct picture changing operators to be inserted in the correlation functions to soak up the zero modes of commuting ghost and we derive the amplitude prescriptions from the coupling with an extended topological gravity on the worldsheet. As an application we consider a simple model on R^(3|2) leading to super-Chern-Simons theory.