Power-Counting Theorem for Non-Local Matrix Models and Renormalisation

By H. Grosse, R. Wulkenhaar. 2003

177 citations recorded by the source corpus.

Solving the exact renormalisation group equation à 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 ℝD in matrix formulation.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2cd6e11b2b3addf7d36d9106e944762b0179f53a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Vanishing of beta function of non-commutative Φ 4 4 theory to all orders (2006, background): “bative renormalizability at all orders has been proved by Grosse, Wulkenhaar and followers [ 4 ][5][6][7].”
Quantized Gauge Theory on the Fuzzy Sphere as Random Matrix Model (2003, background): “A direct quantization l eads to difficulties related to the notorious UV/IR mixing [3], see also [ 4 ] for some recent developments.”