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 ²ⁿ_θ 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 ⁴ 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 ⁴ model.

Key words: Nonperturbative Effects; Non-Commutative Geometry; Matrix Models

E-print number: hep-th/0501174
Cited: by
Refers: to

Received 10 February 2005, accepted for publication 29 March 2005
Published 26 April 2005