F-theory Superspace

TL;DR

This paper develops a linearized superspace formulation of lower-dimensional F-theory, embedding supergravity and matter multiplets, and reveals hidden symmetries and invariances.

Contribution

It provides a detailed linearized superspace framework for F-theory, including supergravity embeddings, gauge invariances, and matter multiplet embeddings.

Findings

Linearized action and gauge transformations for F-theory supergravity.

Identification of Weyl and S-supersymmetry invariances.

Derivation of the F-constraint from gauge invariance.

Abstract

We consider, at the linearized level, the superspace formulation of lower-dimensional F-theory. In particular, we describe the embedding of 3D Type II supergravity of the superstring, or 4D, N=1 supergravity of M-theory, into the corresponding F-theory in full detail, giving the linearized action and gauge transformations in terms of the prepotential. This manifestly supersymmetric formulation reveals some features not evident from a component treatment, such as Weyl and local S-supersymmetry invariances. The linearized multiplet appears as a super 3-form (just as that for the manifestly T-dual theory is a super 2-form), reflecting the embedding of M-theory (as the T-dual theory embeds Type II supergravity). We also give the embedding of matter multiplets into this superspace, and derive the F-constraint from the gauge invariance of the gauge invariance.