Central functions and their physical implications

TL;DR

This paper introduces central functions in quantum field theory to analyze the flow of degrees of freedom from UV to IR, focusing on their behavior in QCD and potential implications for the number of generations.

Contribution

It defines and studies central functions c(g) and c'(g), providing two-loop calculations and exploring their physical implications and duality predictions.

Findings

c(g) and c'(g) flow towards IR as expected in QCD

Two-loop calculations support the IR flow directions

Potential to refine bounds on the number of generations

Abstract

I define central functions c(g) and c'(g) in quantum field theory, useful to study the flow of the numbers of vector, spinor and scalar degrees of freedom from the UV limit to the IR limit and basic ingredients for a description of quantum field theory as an interpolating theory between pairs of 4D conformal field theories. The key importance of the correlator of four stress-energy tensors is outlined in this respect. Then I focus the analysis on the behaviours of the central functions in QCD, computing their slopes in the UV critical point. To two-loops, c(g) and c'(g) point towards the expected IR directions. As a possible physical application, I argue that a closer study of the central functions might allow us to lower the upper bound on the number of generations to the observed value. Candidate all-order expressions for the central functions are compared with the predictions of electric-magnetic duality.