Arguments towards a c-theorem from branch-point twist fields

Castro-Alvaredo, O., Doyon, B. & Levi, E. (2011). Arguments towards a c-theorem from branch-point twist fields. Journal of Physics A: Mathematical and General, 44(49), doi: 10.1088/1751-8113/44/49/492003

Abstract

A fundamental quantity in (1+1)-dimensional quantum field theories is Zamolodchikov's c-function. A function of a renormalization group distance parameter r, which interpolates between ultraviolet and infrared fixed points, its value is usually interpreted as a measure of the number of degrees of freedom of a model at a particular energy scale. The c-theorem establishes that c(r) is a monotonically decreasing function of r and that its derivative may only vanish at quantum critical points (r = 0 and r = ∞). At those points, c(r) becomes the central charge of the conformal field theory which describes the critical point. In this communication, we argue that a different function proposed by Calabrese and Cardy, defined in terms of the two-point function , which involves the branch-point twist field and the trace of the stress–energy tensor Θ, has exactly the same qualitative features as c(r).