Emergent Gravity and Noncommutative Branes from Yang-Mills Matrix Models

TL;DR

This paper advances the understanding of emergent gravity from Yang-Mills matrix models, showing how noncommutative branes lead to a universal effective metric and discussing implications for quantum gravity and cosmology.

Contribution

It develops a covariant formulation of emergent gravity from noncommutative branes in matrix models, highlighting the IKKT model as a quantum gravity candidate.

Findings

Effective metric depends on Poisson structure and embedding.

Derivation of covariant equations of motion.

Discussion of the Planck scale and cosmological constant.

Abstract

The framework of emergent gravity arising from Yang-Mills matrix models is developed further, for general noncommutative branes embedded in R^D. The effective metric on the brane turns out to have a universal form reminiscent of the open string metric, depending on the dynamical Poisson structure and the embedding metric in R^D. A covariant form of the tree-level equations of motion is derived, and the Newtonian limit is discussed. This points to the necessity of branes in higher dimensions. The quantization is discussed qualitatively, which singles out the IKKT model as a prime candidate for a quantum theory of gravity coupled to matter. The Planck scale is then identified with the scale of N=4 SUSY breaking. A mechanism for avoiding the cosmological constant problem is exhibited.