N=2 Sigma Models for Ramond-Ramond Backgrounds

TL;DR

This paper constructs manifestly N=(2,2) supersymmetric sigma models for Type IIB superstrings in Ramond-Ramond backgrounds using the U(4) hybrid formalism, describing both flat and curved target spaces with flux.

Contribution

It introduces a new class of N=2 sigma models with specific Kahler potentials for Ramond-Ramond backgrounds, extending previous formalisms.

Findings

Quadratic Kahler potential yields a free conformal field theory.

Models describe curved target spaces with flux and non-constant dilaton.

Ricci-flat Kahler metric corresponds to on-shell background conditions.

Abstract

Using the U(4) hybrid formalism, manifestly N=(2,2) worldsheet supersymmetric sigma models are constructed for the Type IIB superstring in Ramond-Ramond backgrounds. The Kahler potential in these N=2 sigma models depends on four chiral and antichiral bosonic superfields and two chiral and antichiral fermionic superfields. When the Kahler potential is quadratic, the model is a free conformal field theory which describes a flat ten-dimensional target space with Ramond-Ramond flux and non-constant dilaton. For more general Kahler potentials, the model describes curved target spaces with Ramond-Ramond flux that are not plane-wave backgrounds. Ricci-flatness of the Kahler metric implies the on-shell conditions for the background up to the usual four-loop conformal anomaly.