Center vortices as composites of monopole fluxes S. Deldar, S. M. Hosseini Nejad Department of Physics, University of Tehran [email protected] [email protected]

Abstract Net Using equation for SU(2), we get There are numerical evidences supporting the center vortex theory of And for SU(3) Potential for fundamental confinement. Furthermore, according to Monte Carlo data, monopoles are also representation playing the role of agents of confinement. The induced potential between static sources Creation of a configuration (net) of SU(3) Therefore one can expect some kind of is monopole vacuum linked to a fundamental relations between these two topological representation in a “vortex model” defects. Lattice simulations by Faber and et has the effect of multiplying the Wilson loop by al. [1] show that a center vortex configuration a phase, i.e. after transforming to maximal abelian gauge is the probability that any given unit area and then abelian projection will appear in the is pierced by a center vortex of type n. form of a monopole-antimonopole chain in Abelian monopoles and center Where are monopole charges in equation SU(2) gauge group. Therefore monopoles vortices ----. The static potential induced by nets and center vortices correlate to each other. corresponding to fractional fluxes of the Now we combine fluxes of magnetic charges to In SU(3) gauge group monopoles and monopoles in this “vortex model”, where obtain the center vortex flux. When the center vortices form nets instead of the chains and combinations of them produce center vortex completely contains the minimal area of three vortices may meet at a single point vortex flux is as follows: [2,3]. Motivated by these evidences, we the loop, equations and for SU(2) gauge combine different fluxes of abelian group gives monopoles and obtain the fluxes of center vortices for SU(2) and SU(3) gauge groups. Where We study quark confinement of the Thus, it seems that for SU(2) gauge group the fundamental representation in SU(3) gauge center vortex carries a magnetic flux which is On the other hand, using the thick center vortex group by creating the nets corresponding to equal to the half of the total magnetic flux of a model for large distances, the static potential is fractional fluxes of the monopoles, where monopole. combinations of them may produce center .On the one hand, according to the Monte Carlo vortex fluxes on the minimal area of a Wilson simulations, almost all monopoles are sitting The results are plotted in the figure below. loop in a “center vortex model”. Comparing on top of the vortices by abelian projection [1]. the potential induced by fractional fluxes of monopoles with the one induced by the center vortex model, it seems that the nets of fractional fluxes attract each other. The magnetic charges of abelian monopoles The monopole-vortex junctions are also By a gauge transformation which diagonalizes discussed by Cornwall [2] where they are a scalar in the adjoint representation, called nexuses. In SU(N) gauge group, each monopoles appear in the theory. In SU(2) nexus is a source of N vortices which meet at gauge, the field can be separated into a a point. regular part and a singular part by abelian gauge fixing: Configurations of The free parameters are chosen to be 0.1. As SU(2) monopole vacuum Chain shown in figure, the potential induced by The singular part of the gauge field fractional fluxes of monopoles is linear. corresponds to the magnetic monopole with The extra negative potential energy of static the magnetic charge [4] In SU(3) gauge group, magnetic charges potential induced by center vortex compared satisfy a constraint with the potential induced by fractional fluxes of monopoles shows that the nets corresponding For SU(3) gauge, the topological defects of to fractional fluxes of the monopoles, attract abelian gauge fixing are sources of Therefore the number of independent magnetic each other. magnetic monopoles with magnetic charges reduces to 2. charges equal to: We combine fractional fluxes of magnetic Conclusion charges to obtain a center vortex. When center vortex pierces the minimal area of a We study combinations of monopole fluxes and loop, equations and gives try to obtain a center vortex flux. We use center vortex model and calculate induced potentials Thick Center vortex model from the center vortices and the monoploe In other words, for SU(3) gauge group, the fractional fluxes. Comparing the potentials, we let’s briefly explain the model [5]. The effect vortex carries one third of the total monopole conclude that the fractional fluxes obtained from of a thick center vortex on a fundamental flux plus one third of the total monopole flux monopoles attract each other. Wilson loop is multiplying the loop by a group ,pointing in opposite direction i.e. [1] L. Del Debbio, M. Faber, J. Greensite and S. Olejn´ık, factor Cartan generators in New Developments in , edited Configurations of SU(3) monopole vacuum by P. Damgaard and J. Jurkiewicz (Plenum Press, New York, 1998), p. 47. [2] J. M. Cornwall, Phys. Rev. D 58, 105028 (1998). [3] M. N. Chernodub1 and V. I. Zakharov, Phys. Atom. Dimension of the fundamental representation Net Nucl.72, 2136-2145 (2009). If a thick center vortex is entirely contained [4] G. Ripka, arXiv:hep-ph/0310102v2. within the loop, then [5] M. Faber, J. Greensite, and S. Olejnik, Phys. Rev. D 57, 2603 (1998).

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