Towards SO(2,10)-Invariant M-Theory: Multilagrangian Fields

TL;DR

This paper explores an SO(2,10) covariant extension of M-theory, constructing unitary representations and generalized field theories in 66-dimensional space-time to develop a more symmetric form of 11d supergravity.

Contribution

It introduces a multilagrangian field framework for SO(2,10)-invariant M-theory, highlighting novel gauge invariance and multiple equations of motion for fields.

Findings

Constructed unitary representations in 66d space-time.

Developed a multilagrangian formalism with multiple equations of motion.

Demonstrated gauge and SUSY invariance conditions in the extended theory.

Abstract

The SO(2,10) covariant extension of M-theory superalgebra is considered, with the aim to construct a correspondingly generalized M-theory, or 11d supergravity. For the orbit, corresponding to the $11d$ supergravity multiplet, the simplest unitary representations of the bosonic part of this algebra, with sixth-rank tensor excluded, are constructed on a language of field theory in 66d space-time. The main peculiarities are the presence of more than one equation of motion and corresponding Lagrangians for a given field and that the gauge and SUSY invariances of the theory mean that the sum of variations of these Lagrangians (with different variations of the same field) is equal to zero.