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

TL;DR

This paper discusses a function related to quantum field theories that behaves like the c-function, decreasing monotonically and indicating degrees of freedom, with a focus on branch point twist fields and their relation to the c-theorem.

Contribution

It demonstrates that a function based on branch point twist fields shares the same properties as the c-function, providing new insights into quantum critical points.

Findings

The proposed function decreases monotonically with the RG parameter.

It matches the central charge at critical points.

Supports the validity of the c-theorem using twist fields.

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 that interpolates between UV and IR 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. At those points c(r) becomes the central charge of the conformal field theory which describes the critical point. In this letter we argue that a different function proposed by Calabrese and Cardy, defined in terms of the two-point function of a branch point twist field and the trace of the stress-energy tensor, has exactly the same qualitative features as c(r).