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Fuzzy scalar field theory as a multitrace matrix model

Denjoe O'Connor and Christian Sämann

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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.

Keywords

Field Theories in Lower Dimensions

Matrix Models

Non-Commutative Geometry

PACS

11.25.Yb M theory

11.10.Gh Renormalization

11.10.Cd Axiomatic approach

11.10.Nx Noncommutative field theory

02.10.Ud Linear algebra

02.10.Yn Matrix theory

Subjects

Mathematical physics

Particle physics and field theory

Dates

Issue 08 (August 2007)

Received 27 July 2007, accepted for publication 9 August 2007

Published 23 August 2007



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