Abstract:
It is well known that the potential energy of two heavy quarks
carries an important information about the physics of confinement.
Using the Wilson loop confinement criterion and the Nambu–Goto
string action, this energy can be derived within the bottom-up
holographic approach to strong interactions. We recapitulate the
standard holographic derivation of the potential between two static
sources with emphasis on the physical interpretation of the
results. We address the problem of regularization of the arising
ultraviolet divergence in the general case, with
“ultraviolet” referring to small values of the
holographic coordinate associated with the inverse energy scale in
holographic duality. We show that in the case of the widely used
soft-wall holographic models many ultraviolet divergences can appear
in principle, although the appearance of more than two different
divergences looks somewhat exotic in practice. Some possible
subtraction schemes are discussed. Different schemes lead to a different constant shift of the potential energy, which entails a certain scheme dependence of holographic predictions for the
constant term in the resulting Cornell-like confinement potentials.
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