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 ∂ic = −(gij + Δgij + bij)βj where βj are the beta functions, c and gij are the Zamolodchikov c-function and metric respectively, bij is an antisymmetric tensor introduced by Osborn and Δgij 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.
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