Supergravity in 10 + 2 Dimensions as Consistent Background for Superstring

TL;DR

This paper develops a consistent N=1 supergravity theory in twelve dimensions with signature (10,2), which reduces to ten-dimensional supergravity and supports superstring backgrounds, potentially linking to F-theory.

Contribution

It introduces a twelve-dimensional supergravity framework with null vectors, compatible with superstring backgrounds and supporting F-theory's field theory limit.

Findings

Reproduces 10D supergravity upon reduction

Supports heterotic and type-I superstring backgrounds

Maintains superspace Bianchi identities

Abstract

We present a consistent theory of N=1 supergravity in twelve-dimensions with the signature (10,2). Even though the formulation uses two null vectors violating the manifest Lorentz covariance, all the superspace Bianchi identities are satisfied. After a simple dimensional reduction to ten-dimensions, this theory reproduces the N=1 supergravity in ten-dimensions, supporting the consistency of the system. We also show that our supergravity can be the consistent backgrounds for heterotic or type-I superstring in Green-Schwarz formulation, by confirming the kappa-invariance of the total action. This theory is supposed to be the purely N=1 supergravity sector for the field theory limit of the recently predicted F-theory in twelve-dimensions.