Supermatrix models for M-theory based on osp(1|32,R)

TL;DR

This paper develops supermatrix models based on the osp(1|32,R) algebra, deriving supersymmetry transformations, algebras, and an effective action that extends the BFSS model with additional brane couplings and interactions.

Contribution

It introduces a background-independent osp(1|32,R) cubic matrix model for M-theory, deriving supersymmetry transformations and an effective action including new interaction terms.

Findings

Derived supersymmetry transformations for all fields.

Constructed an osp(1|32,R) matrix model action.

Obtained an effective BFSS-like action with extra couplings and interactions.

Abstract

Taking seriously the hypothesis that the full symmetry algebra of M-theory is osp(1|32,R), we derive the supersymmetry transformations for all fields that appear in 11- and 12-dimensional realizations and give the associated SUSY algebras. We study the background-independent osp(1|32,R) cubic matrix model action expressed in terms of representations of the Lorentz groups SO(10,2) and SO(10,1). We explore further the 11-dimensional case and compute an effective action for the BFSS-like degrees of freedom. We find the usual BFSS action with additional terms incorporating couplings to transverse 5-branes, as well as a mass-term and an infinite tower of higher-order interactions.