Flux-tube ring and glueball properties in the dual Ginzburg-Landau theory

Abstract

An intuitive approach to the glueball using the flux-tube ring solution in the dual Ginzburg-Landau theory is presented. The description of the flux-tube ring as the relativistic closed string with the effective string tension enables us to write the hamiltonian of the flux-tube ring using the Nambu-Goto action.Analyzing the Schrödinger equation, we discuss the mass spectrum and the wave function of the glueball. The lowest glueball state is found to have the mass M G ∼ 1.6 GeV and the size R G ∼ 0.5 fm.

String models of glueballs and the spectrum ofSU(N)gauge theories in2+1dimensions

“…which, with a suitable value for f , will crudely approximate the dependence found in [19]. Performing the integral, and imposing ξ(0) = 0, we have…”

“…This integral cannot be put into closed form, yet we need the inverse function explicitly so as to substitute it into the potential V (ρ(ξ)). While it would be nice to include explicitly the function from [19], any function which approximates it reasonably well will suffice. So rather than using eqn(7) we shall use a less natural form, but one that will suit our manipulations better.…”

“…In this paper we described other ways of including such a cutoff; in particular through a dependence of the string tension on ρ. By taking σ(ρ) from calculations in the literature [19], one can avoid having the additional parameter f to fit. We then pointed out that one should in general include a string curvature term, which for a closed loop will make a contribution γ E /ρ to the effective potential that is of the same form as the Casimir string energy.…”

“…This is motivated by a recent study [19] of closed flux tubes in the dual Ginzburg-Landau theory. They find that the effective string tension, σ ef f (ρ), varies with ρ so as to vanish as ρ → 0.…”

The flux-tube phase transition and bound states at high temperatures

“…where r is the radial coordinate (the distance from the center of the ux tube); n is the integer number associated with the topological charge [26], κ = √ 21. The color-electricˇeld E inside the quarkÄantiquark bound state is given by the rotation of the dual gaugeˇeld…”