Brane compactifications and 4-dimensional geometry in the IKKT model

TL;DR

This paper investigates brane solutions with compact extra dimensions in the IKKT matrix model, analyzing their moduli, fluctuations, and the emergence of gravitational degrees of freedom in 4D spacetime.

Contribution

It provides a detailed study of brane compactifications in the IKKT model, highlighting how fluctuations induce gravitational effects and Ricci-flat metrics.

Findings

Zero modes lead to Ricci-flat 4D metric perturbations

Fluctuations contribute to the effective 4D metric via the Poisson tensor

Coupling to energy-momentum depends on extrinsic curvature

Abstract

We study in detail certain brane solutions with compact extra dimensions M^4 x K in the IKKT matrix model, with K being a two-dimensional rotating torus embedded in R^6. We focus on the compactification moduli and the fluctuations of K \subset R^6 and their physical significance. Mediated by the Poisson tensor, they contribute to the effective 4-dimensional metric on the brane, and thereby become gravitational degrees of freedom. We show that the zero modes corresponding to the global symmetries of the model lead to Ricci-flat 4-dimensional metric perturbations, wherever the energy-momentum tensor vanishes. Their coupling to the energy momentum tensor depends on the extrinsic curvature of the brane.