Supergravity in 10 + 2 Dimensions as Consistent Background for Superstring

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.

An amendment in eq.(3.3a), a paragraph added in pages 6 - 7 with new eq.(3.12), other minor changes like wording and updated references, 14 pages, latex, no figures

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