Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 254, Issue 1, Pages 91-127Publisher
SPRINGER
DOI: 10.1007/s00220-004-1238-9
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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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