Power-counting theorem for non-local matrix models and renormalisation

Details Power-counting theorem for non-local matrix models and renormalisation Power-counting theorem for non-local matrix models and renormalisation

2003-05-08

arxiv.org/abs/hep-th/0305066v4

Commun.Math.Phys. 254 (2005) 91-127

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, 70 figures, LaTeX with svjour macros. v2: proof simplified because a discussion originally designed for \phi^4 on no

Scientific paper

10.1007/s00220-004-1238-9

Solving the exact renormalisation group equation a la Wilson-Polchinski perturbatively, we derive a power-counting theorem for general matrix models with arbitrarily non-local propagators. The power-counting degree is determined by two scaling dimensions of the cut-off propagator and various topological data of ribbon graphs. As a necessary condition for the renormalisability of a model, the two scaling dimensions have to be large enough relative to the dimension of the underlying space. In order to have a renormalisable model one needs additional locality properties--typically arising from orthogonal polynomials--which relate the relevant and marginal interaction coefficients to a finite number of base couplings. The main application of our power-counting theorem is the renormalisation of field theories on noncommutative R^D in matrix formulation.

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