F-theory superspace backgrounds

TL;DR

This paper develops a superspace background framework for F-theory, generalizing current superalgebras to include tensor metrics, enabling a description of F-supergravity and its linearized constraints.

Contribution

It introduces a tensor generalization of the superalgebra metric, allowing the formulation of F-supergravity backgrounds within superspace.

Findings

Derived off-shell linearized superspace constraints for F-theory's massless sector.

Unified description of supergravity theories in various dimensions.

Confirmed consistency with previous formulations without full current algebra.

Abstract

F-theory is the theory proposed to incorporate superstring theory in a way such that STU dualities are manifest. A useful description uses a current superalgebra on a higher-dimensional worldvolume, following from an action for a selfdual gauge field. Here the group "metric" appearing in the Schwinger (central charge) term of this current superalgebra is generalized to a tensor, in analogy to the usual generalization of the structure constants to the torsion (and curvature). This allows introduction of a massless background describing F-supergravity on the original bosonic worldvolume. The isotropy group is represented on superspace, while the (exceptional) symmetry is represented on the worldvolume. As an example, we solve off shell the linearized superspace constraints of the massless sector of the F-theory that generalizes the N=2 supergravity (+ matter) of 3D S(tring)-theory, the corresponding manifestly T-dual theory of T-theory, and the N=1 supergravity of 4D M-theory. The results for the prepotential, its gauge transformation, and action agree with those that were derived previously without reference to the current algebra of the full F-theory.