Sigma model renormalization group flow, 'central charge' action, and Perelman's entropy
- Blackett Laboratory, Imperial College, London SW7 2AZ (United Kingdom)
Zamolodchikov's c-theorem type argument (and also string theory effective action constructions) imply that the RG flow in 2d sigma model should be a gradient one to all loop orders. However, the monotonicity of the flow of the target-space metric is not obvious since the metric on the space of metric-dilaton couplings is indefinite. To leading (one-loop) order when the RG flow is simply the Ricci flow the monotonicity was proved by Perelman [G. Perelman, math.dg/0211159.] by constructing an 'entropy' functional which is essentially the metric-dilaton action extremized with respect to the dilaton with a condition that the target-space volume is fixed. We discuss how to generalize the Perelman's construction to all loop orders (i.e. all orders in {alpha}{sup '}). The resulting entropy is equal to minus the central charge at the fixed points, in agreement with the general claim of the c-theorem.
- OSTI ID:
- 21020170
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 75, Issue 6; Other Information: DOI: 10.1103/PhysRevD.75.064024; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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