Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-01-21
JHEP 0503 (2005) 075
Physics
High Energy Physics
High Energy Physics - Theory
38 pages, 1 figure. V2: references added. V3: typos fixed, discussion added; published version
Scientific paper
10.1088/1126-6708/2005/03/075
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 R^{2n}_\theta 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 \phi^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 \phi^4 model.
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