Center-vortex solutions of the Yang-Mills effective action in three and four dimensions

Abstract

We calculate the one-loop effective action of the SU (2) Yang-Mills theory for center-vortex configurations, both in 3d and 4d. We find that in both cases there are minima of the effective action, corresponding to vortices of the transverse size approximately 4/g 2 3 and 1.7/Λ M S , respectively. The values of the effective actions at the minima are negative, suggesting that the Euclidian vacuum may be unstable with respect to creation of vortices.

Energy density of vortices in the Schrödinger picture

“…In a realistic vortex model of the QCD vacuum, energy densities of the type considered here are but one among a whole set of factors influencing vortex dynamics. For example, realistic vortices are not infinitely thin, but are smeared out to a finite transverse thickness, a case which has recently also been discussed [12,13]. As shown there, a finite thickness can actually lead to a lowering of the effective energy density below the one of the perturbative vacuum.…”

“…[12,13] for thick center vortices and [14] for thin vortices of arbitrary flux. In the present paper, we expand on these investigations, which only considered gluonic fluctuations to one-loop order, by evaluating the one-loop energy density of an infinitely thin static magnetic vortex including quark fluctuations.…”

The confinement problem in lattice gauge theory

“…The situation changes however, as shown by Diakonov and Maul [67], when quantum corrections at one-loop order are included. Diakonov and Maul calculate the Yang-Mills effection action, to one loop order, of the following configuration (in cylindrical coordinates)…”

Confinement from Center Vortices: A review of old and new results

“…Center vortices, unlike instantons (and their finite temperature cousins, the calorons) are definitely not saddlepoints of the classical action. But matters are different at one loop, and the old work of Ambjorn and Olesen [9], and later work by Diakonov and Maul [10], both suggest that center vortices are saddlepoints of the effective action at one-loop level. There is also a simple argument based on lattice theory: Consider a lattice action with traces in the fundamental (F) and adjoint (A) representations…”