### Abstract

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 ?_{i}c = -(g_{ij} + ?g_{ij} + b _{ij})ß^{j} where ß^{j} are the beta functions, c and g_{ij} are the Zamolodchikov c-function and metric respectively, b_{ij} is an antisymmetric tensor introduced by Osborn and ?g_{ij} is a certain metric correction. The formula is derived under the assumption of stress-energy conservation and certain conditions on the infrared behavior 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. Being specialized to nonlinear sigma models this formula implies a one-to-one correspondence between renormalization group fixed points and critical points of c. © 2010 IOP Publishing Ltd.

Original language | English |
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Article number | 215401 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 43 |

Issue number | 21 |

DOIs | |

Publication status | Published - 2010 |