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

Harald Grosse·Raimar Wulkenhaar
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Abstract

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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Harald Grosse, Raimar Wulkenhaar. 2004-10-04. Power-counting theorem for non-local matrix models and renormalisation. https://doi.org/10.1007/s00220-004-1238-9

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