On matrix geometry

Details On matrix geometry On matrix geometry

2011-01-26

arxiv.org/abs/1101.5003v2

PoS CNCFG2010:031,2011

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

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.

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