Demons and Abelian Projection QCD: Action and Crossover

TL;DR

This paper evaluates the exact action of Abelian projection QCD using the demon method, revealing that QCD monopoles are pointlike and challenging previous effective condensation models.

Contribution

It provides a novel, assumption-free analysis of Abelian projection QCD's action, showing monopoles are pointlike rather than extended objects.

Findings

At strong coupling, the action resembles 1x1 compact QED.

Coefficients for larger plaquettes vanish at all beta_{SU2}.

QCD monopoles are pointlike, not extended objects.

Abstract

I evaluate S_{APQCD}, the exact action of Abelian projection QCD, using the microcanonical demon method. Starting with a trial action consisting of L=1, L=2, & L=3 LxL plaquettes plus a Smit-van-der-Sijs magnetic monopole ``mass'' operator, I show that coefficients of the L=2 and L=3 plaquettes vanish at all beta_{SU2}. In fact, at strong coupling S_{APQCD} is essentially the 1x1 compact QED action with beta_{U1}=beta_{SU2}/2. Beyond beta_{SU2}>=2, S_{APQCD} gains an exogenous negative 1x1x1 magnetic monopole mass shift. Note that my approach differs fundamentally from the Smit-van-der-Sijs approach in that I do not make an a priori assumption about monopole or plaquette size in S_{APQCD}. Indeed, these results suggest that QCD monopoles are pointlike, in contrast to the ``effective'' condensation picture put forth by Smit and van der Sijs.