Ph. de Forcrand

I present a unified picture of center vortices and Abelian monopoles. Both appear as local gauge ambiguities in the Laplacian Center Gauge. This gauge is constructed for a general SU (N) theory. Numerical evidence is presented, for SU (2) and SU (3), that the projected Z N theory confines with a string tension similar to the non-Abelian one. 1 Motivation and technical problem The road traveled by physicists in their efforts to identify the effective, InfraRed degrees of freedom of QCD is far from straight. It bifurcates in many directions, most of which are still under exploration. Currently, the two most popular effective descriptions of confinement are in terms of Abelian monopoles 1,2 and center vortices 3,4. I want to show that these two descriptions can be unified: these two branches of the road merge together, perhaps indicating that we are traveling towards a piece of Truth. The study of center vortices, first proposed by Mack 4 and by 't Hooft 3 , has been revived by Greensite and collaborators. They project the SU (2) lattice gauge theory to a Z 2 gauge theory, by partially fixing the gauge to Maximal Center Gauge, defined as the gauge in which x,µ |T r U µ (x)| 2 maximum. (1) In this gauge, the center-projected links are z µ (x) ≡ sign(T r U µ (x)). This Z 2 theory has defects corresponding to plaquettes taking value −1. Greensite et al. 5 showed that the string tension σ given by these defects closely matches that of the original SU (2) theory. Being skeptical about this, I investigated with M. D'Elia the coset theory, made of positive-trace links U ′ µ (x) ≡ z µ (x) U µ (x). This theory has more short-range disorder than the original one, but carries a presented by Ph. de Forcrand.