Is There a Stringy Description of Self-Dual Supergravity in 2+2 Dimensions?

TL;DR

This paper explores string theory models in 2+2 dimensions aiming to describe self-dual supergravity, but finds that current constructions do not match the expected supergravity interactions, indicating the need for more general approaches.

Contribution

The authors constructed two N=2 string theories with superspace target spaces to model self-dual supergravity, revealing limitations in their interaction structures.

Findings

Constructed two N=2 string theories with superspace targets.

Found that interactions do not match self-dual supergravity.

Indicated that more general constructions are necessary.

Abstract

The well known N=2 string theory describes self-dual gravity, as was shown by Ooguri and Vafa sometime ago. In search of a variant of this theory which would describe self-dual supergravity in 2+2 dimensions, we have constructed two new N=2 strings theories in which the target space is a superspace. Both theories contain massless scalar and spinor fields in their spectrum, and one of them has spacetime supersymmetry. However, we find that the interactions of these fields do not correspond to those of self-dual supergravity. In our construction, we have used the basic (2,2) superspace variables, and considered quadratic constraints in these variables. A more general construction may be needed for a stringy description of self-dual supergravity.