Dynamical phase space from a SO(d,d) matrix model

TL;DR

This paper introduces a SO(d,d) matrix model derived from a generalized Yang-Mills theory that captures spacetime and phase space dynamics, offering new insights into emergent gravity and quantum mechanics.

Contribution

It presents a novel SO(d,d) matrix model from a Courant algebroid-based Yang-Mills theory, linking matrix models to phase space and emergent gravity.

Findings

Model captures dynamics of spacetime and phase space

Classical solutions correspond to noncommutative curved manifolds

Suggests a new mechanism for emergent gravity

Abstract

It is shown that a matrix model with SO(d,d) global symmetry is derived from a generalized Yang-Mills theory on the standard Courant algebroid. This model keeps all the positive features of the well-studied type IIB matrix model, and it has many additional welcome properties. We show that it does not only capture the dynamics of spacetime, but it should be associated with the dynamics of phase space. This is supported by a large set of classical solutions of its equations of motion, which corresponds to phase spaces of noncommutative curved manifolds and points to a new mechanism of emergent gravity. The model possesses an additional symmetry that exchanges positions and momenta, in analogy to quantum mechanics. It is argued that the emergence of phase space in the model is an essential feature for the investigation of the precise relation of matrix models to string theory and quantum gravity.