Abstract
In this work we perform an investigation of the flux tube between two static color sources in four dimensional $SU(3)$ Yang-Mills theory, using the so called connected correlator. Contrary to most previous studies we do not use any smoothing algorithm to facilitate the evaluation of the correlator, that is performed using only stochastically exact techniques. We first examine the renormalization properties of the connected operator, then we present our numerical data for the longitudinal chromoelectric component of the flux tube, that are used to extract the dual superconductivity parameters.
Highlights
The investigation of the color flux tubes connecting static sources in non-Abelian gauge theories has become a standard tool to study color confinement [1,2,3,4,5,6,7,8,9,10,11,12,13]
A quantity that satisfies this requirement can be built by using the correlator of a Polyakov loops pair with a plaquette: the pair of Polyakov loops represents a couple of static color charges while the plaquette probes the field strength in the background of the static charges
The connected correlator defined in Eq (2) can be estimated by using a combination of multihit [31] and multilevel [32] techniques: multihit can be applied to the links of the Polyakov loops and to a single link of the plaquette
Summary
The investigation of the color flux tubes connecting static sources in non-Abelian gauge theories has become a standard tool to study color confinement [1,2,3,4,5,6,7,8,9,10,11,12,13]. In lattice simulations, color sources are seen to be connected by tube-like structures for all the values of the coupling constant (at zero temperature). This is a strong indication that the mechanism responsible for color confinement is the same at weak and at strong coupling, in which limit color flux tubes naturally emerge [14], and the area-law of the Wilson loops can be analytically proven [15]. To study flux tubes on the lattice we need an observable whose average value will provide us information about the flux tube details: the value of this observable has to be related to that of the field strength in the background of a couple of static color sources.
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