English

On matrix geometry

High Energy Physics - Theory 2015-03-18 v2 General Relativity and Quantum Cosmology Mathematical Physics math.MP

Abstract

The foundations of matrix geometry are discussed, which provides the basis for recent progress on the effective geometry and gravity in Yang-Mills matrix models. Basic examples lead to a notion of embedded noncommutative spaces (branes) with emergent Riemannian geometry. This class of configurations turns out to be preserved under small deformations, and is therefore appropriate for matrix models. The relation with spectral geometry is discussed. A possible realization of sufficiently generic 4-dimensional geometries as noncommutative branes in D=10 matrix models is sketched.

Keywords

Cite

@article{arxiv.1101.5003,
  title  = {On matrix geometry},
  author = {Harold Steinacker},
  journal= {arXiv preprint arXiv:1101.5003},
  year   = {2015}
}

Comments

Contribution to the proceedings of the Corfu Summer Institute on Elementary Particles and Physics 2011. 15 pages. V2: minor reformulations

R2 v1 2026-06-21T17:17:14.088Z