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Holographic Confinement of the Solitary Quark

Single quarks moving in the vacuum of confining gauge theories are stopped by a drag force. The holographic description relates the confining scale in the bulk geometry with a range of physical values for the drag force in the vacuum. The vacuum drag force acting on the isolated quark directly manifests quark confinement since it prevents the quark from walking freely in the vacuum. However, analytical expressions for the drag force as a function of the quark velocity were lacking. In the present work, we propose that the vacuum drag force is given by the regularized zero-temperature limit of the corresponding thermal drag force. Within this approach, we obtain the desired analytic expressions in two different holographic models: the quadratic dilaton and the D-instanton. In both cases, we find well-behaved functions belonging to their physical range of values.