A non-perturbative approach to non-commutative scalar field theory

Published 26 April 2005 Published under licence by IOP Publishing Ltd
, , Citation Harold Steinacker JHEP03(2005)075 DOI 10.1088/1126-6708/2005/03/075

1126-6708/2005/03/075

Abstract

Non-commutative euclidean scalar field theory is shown to have an eigenvalue sector which is dominated by a well-defined eigenvalue density, and can be described by a matrix model. This is established using regularizations of Bbb R2nθ via fuzzy spaces for the free and weakly coupled case, and extends naturally to the non-perturbative domain. It allows to study the renormalization of the effective potential using matrix model techniques, and is closely related to UV/IR mixing. In particular we find a phase transition for the ϕ4 model at strong coupling, to a phase which is identified with the striped or matrix phase. The method is expected to be applicable in 4 dimensions, where a critical line is found which terminates at a non-trivial point, with nonzero critical coupling. This provides evidence for a non-trivial fixed-point for the 4-dimensional NC ϕ4 model.

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10.1088/1126-6708/2005/03/075