On an (Interacting) Field Theories With Tensorial Momentum

TL;DR

This paper extends the construction of tensorial space-time field theories to include interactions, specifically deriving unique cubic interaction terms for SO(2,2) gravity that preserve gauge invariance.

Contribution

It introduces the first interacting tensorial space-time field theory with gauge invariance, expanding previous non-interacting models to include consistent interactions.

Findings

Derived unique cubic interaction terms for SO(2,2) gravity

Maintained gauge invariance in the interacting theory

Extended tensorial space-time models to include interactions

Abstract

The construction of field theories with space-time symmetries, including tensorial charges (i.e. of M-theory type), initiated in hep-th/9907011, is extended to include interaction. For SO(2,2) gravity in a tensorial space-time, with space-time symmetry consisting of Lorentz generators and "translations", represented by second-rank antisymmetric tensor, the cubic interaction terms are constructed by requirement of maintaining the gauge invariance property of theory. This interaction is essentially unique.