Gravity and compactified branes in matrix models

TL;DR

This paper demonstrates how emergent gravity can arise from Yang-Mills matrix models through compactified branes with split noncommutativity, linking moduli of compactification to gravitational dynamics without traditional Einstein-Hilbert terms.

Contribution

It introduces a novel mechanism for emergent gravity in matrix models using compactified branes and split noncommutativity, avoiding the need for Einstein-Hilbert action.

Findings

Newtonian gravity can emerge from matrix models.

Effective Newton constant depends on noncommutativity scale.

Perturbative finiteness suggested for the IKKT model.

Abstract

A mechanism for emergent gravity on brane solutions in Yang-Mills matrix models is exhibited. Newtonian gravity and a partial relation between the Einstein tensor and the energy-momentum tensor can arise from the basic matrix model action, without invoking an Einstein-Hilbert-type term. The key requirements are compactified extra dimensions with extrinsic curvature M^4 x K \subset R^D and split noncommutativity, with a Poisson tensor \theta^{ab} linking the compact with the noncompact directions. The moduli of the compactification provide the dominant degrees of freedom for gravity, which are transmitted to the 4 noncompact directions via the Poisson tensor. The effective Newton constant is determined by the scale of noncommutativity and the compactification. This gravity theory is well suited for quantization, and argued to be perturbatively finite for the IKKT model. Since no compactification of the target space is needed, it might provide a way to avoid the landscape problem in string theory.