Supergravity Theories in $D\ge 12$ Coupled to Super p-Branes

TL;DR

This paper develops supergravity theories in 12 and 13 dimensions with specific signatures, coupling them to super p-branes, and introduces a covariant formulation using scalar superfields to maintain Lorentz symmetry.

Contribution

It constructs new supergravity models in higher dimensions coupled to super p-branes, employing scalar superfields to preserve covariance and consistency.

Findings

Successfully formulated supergravity in 12 and 13 dimensions with specific signatures.

Coupled supergravity theories to superstring, super (2+2)-brane, and supermembrane.

Maintained Lorentz covariance using scalar superfields and modified Lorentz generators.

Abstract

We construct supergravity theories in twelve and thirteen dimensions with the respective signatures (10,2) and (11,2) with some technical details. Starting with N=1 supergravity in 10+2 dimensions coupled to Green-Schwarz superstring, we give N=2 chiral supergravity in 10+2 dimensions with its couplings to super (2+2)-brane. We also build an N=1 supergravity in 11+2 dimensions, coupled to supermembrane. All of these formulations utilize scalar (super)fields intact under supersymmetry, replacing the null-vectors introduced in their original formulations. This method makes all the equations SO(10,2) or SO(11,2) Lorentz covariant, up to modified Lorentz generators. We inspect the internal consistency of these formulations, in particular with the usage of the modified Lorentz generators for the extra coordinates.