Matrix Models in Homogeneous Spaces

TL;DR

This paper explores the construction of non-commutative gauge theories on homogeneous spaces using matrix models, specifically analyzing the CP^2 case and its relation to the IIB matrix model in the large N limit.

Contribution

It introduces a method to formulate non-commutative gauge theories on homogeneous spaces via cubic terms in the IIB matrix model, expanding the understanding of gauge theories in non-commutative geometry.

Findings

Constructed non-commutative gauge theories on G/H spaces.

Demonstrated the realization of R^4 gauge theory in the large N limit.

Connected these theories to the large N limit of the IIB matrix model.

Abstract

We investigate non-commutative gauge theories in homogeneous spaces G/H. We construct such theories by adding cubic terms to IIB matrix model which contain the structure constants of G. The isometry of a homogeneous space, G must be a subgroup of SO(10) in our construction. We investigate CP^2=SU(3)/U(2) case in detail which gives rise to 4 dimensional non-commutative gauge theory. We show that non-commutative gauge theory on R^4 can be realized in the large N limit by letting the action approach IIB matrix model in a definite way. We discuss possible relevances of these theories to the large N limit of IIB matrix model.