Abstract
We extend the holographic trailing string picture of a heavy quark to the case of a bulk geometry dual to a confining gauge theory. We compute the classical trailing confining string solution for a static as well as a uniformly moving quark. The trailing string is infinitely extended and approaches a confining horizon, situated at a critical value of the radial coordinate, along one of the space-time directions, breaking boundary rotational invariance. We compute the equations for the fluctuations around the classical solutions, which are used to obtain boundary force correlators controlling the Langevin dynamics of the quark. The imaginary part of the correlators has a non-trivial low-frequency limit, which gives rise to a viscous friction coefficient induced by the confining vacuum. The vacuum correlators are used to define finite-temperature dressed Langevin correlators with an appropriate high-frequency behavior.
Highlights
The AdS/CFT correspondence, or holographic gauge/gravity duality, has offered a new way of looking at quantum large-N gauge theories in the strongly-coupled regime, providing a reformulation in terms of degrees of freedom propagating in a higher-dimensional, curved space-time
We extend the holographic trailing string picture of a heavy quark to the case of a bulk geometry dual to a confining gauge theory
The AdS/CFT duality, already in its simplest form, offers a way to compute the coefficients η and κ entering the Langevin equation. This has been carried out in the case of the supersymmetric and conformally invariant N = 4 Super-Yang-Mills theory, in a series of papers [11,12,13,14,15,16,17,18,19,20] in which a heavy quark moving at constant velocity v is mapped holographically into a classical string extending into the bulk AdS-Schwarzschild black hole geometry, and trailing its uniformly moving endpoint, that represents the boundary quark
Summary
The AdS/CFT correspondence, or holographic gauge/gravity duality, has offered a new way of looking at quantum large-N gauge theories in the strongly-coupled regime, providing a reformulation in terms of degrees of freedom propagating in a higher-dimensional, curved space-time. The AdS/CFT duality, already in its simplest form, offers a way to compute the coefficients η and κ entering the Langevin equation This has been carried out in the case of the supersymmetric and conformally invariant N = 4 Super-Yang-Mills theory, in a series of papers [11,12,13,14,15,16,17,18,19,20] in which a heavy quark moving at constant velocity v is mapped holographically into a classical string extending into the bulk AdS-Schwarzschild black hole geometry, and trailing its uniformly moving endpoint, that represents the boundary quark. The latter are effectively two-dimensional bulk fields living on the string world-sheet, and the retarded correlators are computed by the standard prescription giving in-falling boundary conditions at the (world-sheet) horizon
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