Power counting theorem for nonlocal matrix models and renormalization
May, 2003Citations per year
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.Note:
- 35 pages, 70 figures, LaTeX with svjour macros. v2: proof simplified because a discussion originally designed for \phi^4 on noncommutative R^2 was actually not necessary, see hep-th/0307017. v3: consistency conditions removed because models of interest relate automatically the relevant/marginal interactions to a finite number of base couplings, see hep-th/0401128. v4: integration procedure improved so that the initial cut-off can be directly removed: to appear in Commun. Math. Phys
- matrix model
- renormalization group
- Feynman graph: higher-order
- propagator
- phi**n model: 4
- space-time: noncommutative
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