Fuzzy scalar field theory as a multitrace matrix model

O'Connor, Denjoe and Sämann, Christian (2007) Fuzzy scalar field theory as a multitrace matrix model. Journal of High Energy Physics, 2007 (08). 066-066. ISSN 1029-8479

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Official URL: http://doi.org/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.

Item Type: Article
Uncontrolled Keywords: Matrix Models, Noncommutative Geometry, Field Theories in Lower Dimensions
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 05 Oct 2017 19:31
Last Modified: 20 Dec 2022 09:01
Identification Number: DIAS-STP-07-11
URI: https://dair.dias.ie/id/eprint/204

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