Split noncommutativity and compactified brane solutions in matrix models

TL;DR

This paper constructs and analyzes solutions in matrix models where noncommutativity links compact and non-compact spaces, stabilizing extra dimensions and revealing emergent gravity and gauge theories.

Contribution

It introduces explicit solutions with stabilized extra dimensions in matrix models, demonstrating noncommutative geometry's role in emergent gravity and gauge theories.

Findings

Solutions with R^{3,1} x K structure are explicitly constructed.

Extra dimensions are stabilized by angular momentum.

Emergent gravity and gauge theories arise from deformations of solutions.

Abstract

Solutions of the undeformed IKKT matrix model with structure R^{3,1} x K are presented, where the noncommutativity relates the compact with the non-compact space. The extra dimensions are stabilized by angular momentum, and the scales of K are generic moduli of the solutions. Explicit solutions are given for K= T^2, K= T^4, K = S^2 x T^2 and K = S^2 x S^2. Infinite towers of Kaluza-Klein modes may arise in some directions, along with an effective UV cutoff on the non-compact space. Deformations of these solutions carry NC gauge theory coupled to (emergent) gravity. Analogous solutions of the BFSS model are also given.