Gradient formula for the beta function of 2D quantum field theory

Daniel Friedan, Anatoly Konechny

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


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 ?ic = -(gij + ?gij + b ijj where ßj are the beta functions, c and gij are the Zamolodchikov c-function and metric respectively, bij is an antisymmetric tensor introduced by Osborn and ?gij 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 languageEnglish
Article number215401
JournalJournal of Physics A: Mathematical and Theoretical
Issue number21
Publication statusPublished - 2010


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