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Gradient formula for the beta-function of 2d quantum field theory · Around

2009

Gradient formula for the beta-function of 2d quantum field theory

Friedan, Daniel, Konechny, Anatoly

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We give a non-perturbative proof of a gradient formula for beta functions of two-dimensional quantum field theories.

The gradient formula has the form \partial_{i}c = - (g_{ij}+\Delta g_{ij} +b_{ij})\beta^{j} where \beta^{j} are the beta functions, c and g_{ij} are the Zamolodchikov c-function and metric, b_{ij} is an antisymmetric tensor introduced by H.
Osborn and \Delta g_{ij} is a certain metric correction.
The formula is derived under the assumption of stress-energy conservation and certain conditions on the infrared behaviour the most significant of which is the condition that the large distance limit of the field theory does not exhibit spontaneously broken global conformal symmetry.

Built on

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Then

G.Curci and G.Paffuti,
1987
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H. Osborn,
1988
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H. Osborn,
1990
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H. Osborn,
1991
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A. Cappelli, D. Friedan and J. I. Latorre,
1991
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I. Affleck and A. Ludwig,
1991
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D. Friedan and A. Konechny,
2004
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D. Z. Freedman, M. Headrick and A. Lawrence,
2006

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