Curvature and Gravity Actions for Matrix Models II: the case of general Poisson structure

TL;DR

This paper explores the geometric interpretation of higher-order terms in matrix models of Yang-Mills type, extending previous work to 4D geometries with general Poisson structures, and identifies their relation to intrinsic and extrinsic curvature effects.

Contribution

It generalizes earlier results to 4-dimensional space-times with arbitrary Poisson structures, revealing how higher-order terms relate to geometry and curvature in matrix models.

Findings

Identifies terms depending solely on intrinsic geometry and curvature.

Discovers a mechanism where the effective metric nearly matches the induced metric.

Shows deviations are suppressed and linked to U(1) gauge fields.

Abstract

We study the geometrical meaning of higher-order terms in matrix models of Yang-Mills type in the semi-classical limit, generalizing recent results arXiv:1003.4132 to the case of 4-dimensional space-time geometries with general Poisson structure. Such terms are expected to arise e.g. upon quantization of the IKKT-type models. We identify terms which depend only on the intrinsic geometry and curvature, including modified versions of the Einstein-Hilbert action, as well as terms which depend on the extrinsic curvature. Furthermore, a mechanism is found which implies that the effective metric G on the space-time brane M \subset R^D "almost" coincides with the induced metric g. Deviations from G=g are suppressed, and characterized by the would-be U(1) gauge field.