The curvature of branes, currents and gravity in matrix models

TL;DR

This paper explores how gravity emerges on branes within Yang-Mills matrix models, relating curvature to conserved currents and energy-momentum without traditional gravitational actions, and highlighting the role of extrinsic curvature and symmetries.

Contribution

It establishes a novel relation between Ricci curvature and energy-momentum in matrix models, linking effective gravity to brane embedding and compactification moduli without Einstein-Hilbert terms.

Findings

Curvature expressed via conserved currents

Relation between Ricci tensor and energy-momentum tensor

Gravity coupling governed by extrinsic curvature

Abstract

The curvature of brane solutions in Yang-Mills matrix models is expressed in terms of conserved currents associated with global symmetries of the model. This implies a relation between the Ricci tensor and the energy-momentum tensor due to the basic matrix model action, without invoking an Einstein-Hilbert term. The coupling is governed by the extrinsic curvature of the brane embedding, which arises naturally for compactified brane solutions. The effective gravity on the brane is thereby related to the compactification moduli, and protected from quantum corrections due to the relation with global symmetries.