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 ij)ßj 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.
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Publication status||Published - 2010|