Fuzzy Scalar Field Theory as a Multitrace Matrix Model

Details Fuzzy Scalar Field Theory as a Multitrace Matrix Model Fuzzy Scalar Field Theory as a Multitrace Matrix Model

2007-06-17

arxiv.org/abs/0706.2493v2

JHEP 0708:066,2007

Physics

High Energy Physics

High Energy Physics - Theory

1+25 pages, replaced with published version, minor improvements

Scientific paper

10.1088/1126-6708/2007/08/066

We develop an analytical approach to scalar field theory on the fuzzy sphere based on considering a perturbative expansion of the kinetic term. This expansion allows us to integrate out the angular degrees of freedom in the hermitian matrices encoding the scalar field. The remaining model depends only on the eigenvalues of the matrices and corresponds to a multitrace hermitian matrix model. Such a model can be solved by standard techniques as e.g. the saddle-point approximation. We evaluate the perturbative expansion up to second order and present the one-cut solution of the saddle-point approximation in the large N limit. We apply our approach to a model which has been proposed as an appropriate regularization of scalar field theory on the plane within the framework of fuzzy geometry.

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