The Matrix Model for M Theory as an Exemplar of Trace (or Generalized Quantum) Dynamics

TL;DR

This paper demonstrates that the matrix model for M theory adheres to generalized quantum dynamics principles, enabling operator-based supersymmetry calculations and broadening the understanding of supersymmetric trace dynamics.

Contribution

It shows the M theory matrix model obeys trace dynamics assumptions, allowing supersymmetry verification and algebra calculation without matrix element reference.

Findings

Supersymmetry can be verified as an operator calculation.

Supercharge algebra can be computed using generalized Poisson brackets.

The results extend to all rigid supersymmetry theories within trace dynamics.

Abstract

We show that the recently proposed matrix model for M theory obeys the cyclic trace assumptions underlying generalized quantum or trace dynamics. This permits a verification of supersymmetry as an operator calculation, and a calculation of the supercharge density algebra by using the generalized Poisson bracket, in a basis-independent manner that makes no reference to individual matrix elements. Implications for quantization of the model are discussed. Our results are a special case of a general result presented elsewhere, that all rigid supersymmetry theories can be extended to give supersymmetric trace dynamics theories, in which the supersymmetry algebra is represented by the generalized Poisson bracket of trace supercharges, constructed from fields that form a noncommutative trace class graded operator algebra.