Do the critical (2,2) strings know about a supergravity in 2+10 dimensions ?

TL;DR

This paper explores the integrability and symmetries of a (2,2) string theory in 2+10 dimensions, proposing a connection to a hypothetical supergravity theory based on the structure of F-brane actions.

Contribution

It demonstrates the integrability of the effective equations for a mixed open-closed string theory and links the F-brane action to a conjectured supergravity in 2+10 dimensions.

Findings

Effective equations are integrable for abelian gauge groups.

The Born-Infeld-type action is non-covariant and related to F-brane dynamics.

Symmetries suggest a connection to a self-dual supergravity in higher dimensions.

Abstract

The effective field equations of motion for a mixed theory of open and closed (2,2) world-sheet supersymmetric critical strings are shown to be integrable in the case of an abelian gauge group. The Born-Infeld-type effective action in 2+2 dimensions is intrinsically non-covariant, and it can be interpreted as (a part of) the F-brane world-volume action. The covariant F-brane action is unambiguously restored by its maximal (N=8) world-volume supersymmetry. The 32 supercharges, the local SO(2,1) x SO(8) and rigid SL(2,R) symmetries of the F-brane action naturally suggest its interpretation as the hypothetical (non-covariant) self-dual `heterotic' (1,0) supergravity in 2+10 dimensions.