The cubic matrix model and a duality between strings and loops

TL;DR

This paper proposes a duality between matrix formulations of M theory and an extended loop quantum gravity, based on a cubic matrix model with new compactifications involving a supersymmetric quantum group extension.

Contribution

It introduces a novel duality connecting M theory matrix models with a background independent loop quantum gravity extension using a supersymmetric quantum group.

Findings

New compactifications with SU(16) conformal blocks

Breaking of SU(N) symmetry while preserving SU(16)

Dual description of M theory degrees of freedom

Abstract

We find evidence for a duality between the standard matrix formulations of M theory and a background independent theory which extends loop quantum gravity by replacing SU(2) with a supersymmetric and quantum group extension of SU(16). This is deduced from the recently proposed cubic matrix model for M theory which has been argued to have compactifications which reduce to the IKKT and dWHN-BFSS matrix models. Here we find new compactifications of this theory whose Hilbert spaces consist of SU(16) conformal blocks on compact two-surfaces. These compactifications break the SU(N) symmetry of the standard M theory compactifications, while preserving SU(16), while the BFSS model preserve the SU(N) but break SU(16) to the SO(9) symmetry of the 11 dimensional light cone coordinates. These results suggest that the supersymmetric and quantum deformed SU(16) extension of loop quantum gravity provides a dual, background independent description of the degrees of freedom and dynamics of the M theory matrix models.