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Title: Sigma model renormalization group flow, 'central charge' action, and Perelman's entropy

Abstract

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.

Authors:
 [1]
  1. Blackett Laboratory, Imperial College, London SW7 2AZ (United Kingdom)
Publication Date:
OSTI Identifier:
21020170
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.75.064024; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACTION INTEGRAL; COUPLING; ENTROPY; METRICS; QUANTUM FIELD THEORY; RENORMALIZATION; SIGMA MODEL; SPACE; STRING MODELS

Citation Formats

Tseytlin, A. A.. Sigma model renormalization group flow, 'central charge' action, and Perelman's entropy. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.064024.
Tseytlin, A. A.. Sigma model renormalization group flow, 'central charge' action, and Perelman's entropy. United States. doi:10.1103/PHYSREVD.75.064024.
Tseytlin, A. A.. Thu . "Sigma model renormalization group flow, 'central charge' action, and Perelman's entropy". United States. doi:10.1103/PHYSREVD.75.064024.
@article{osti_21020170,
title = {Sigma model renormalization group flow, 'central charge' action, and Perelman's entropy},
author = {Tseytlin, A. A.},
abstractNote = {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.},
doi = {10.1103/PHYSREVD.75.064024},
journal = {Physical Review. D, Particles Fields},
number = 6,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}