Special Geometries Emerging from Yang-Mills Type Matrix Models

TL;DR

This paper reviews how different geometries like Schwarzschild and Reissner-Nordstroem can emerge from Yang-Mills matrix models with branes, including their embeddings and non-commutative structures, motivated by effective actions resembling Einstein-Hilbert gravity.

Contribution

It demonstrates the emergence of classical geometries from matrix models and details their embeddings and non-commutative structures, linking to gravitational actions.

Findings

Emergence of Schwarzschild and Reissner-Nordstroem geometries from matrix models

Explicit brane embeddings and non-commutative structures provided

Effective actions resemble Einstein-Hilbert gravity

Abstract

I review some recent results which demonstrate how various geometries, such as Schwarzschild and Reissner-Nordstroem, can emerge from Yang-Mills type matrix models with branes. Furthermore, explicit embeddings of these branes as well as appropriate Poisson structures and star-products which determine the non-commutativity of space-time are provided. These structures are motivated by higher order terms in the effective matrix model action which semi-classically lead to an Einstein-Hilbert type action.