How to get rid of Dirac worldsheets in the Cho–Faddeev–Niemi representation of SU(2) Yang–Mills theory

Abstract

In this paper, we present an exact procedure to deal with Dirac strings or worldsheets in gauge theories containing ensembles of monopoles interacting with charged fields. For SU(2) Yang–Mills theory, initially we construct the appropriate change of variables of the charged fields (including charged ghosts and auxiliary fields) so that the only change in the integrand of the partition function, in the maximal Abelian gauge, is the addition of given closed Dirac worldsheets. Next, we derive our main result, namely we show that it is always possible to choose them in such a manner that the total (open plus closed) Dirac worldsheets explicitly decouple from the charged sector, leaving only the effect of their associated gauge invariant borders (where the monopoles are placed), without missing any information about the center vortex sector. This procedure serves as a simplifying basis to deal with ensembles of monopoles and center vortices in the framework of the Cho–Faddeev–Niemi gauge field decomposition, by writing the partition function only in terms of the physical part of the defects to be integrated.