Holography and the internal structure of charmonium

Holographic models that consider classical vector fields in a 5-d background provide successful effective descriptions for heavy vector meson spectra. This holds both in the vacuum and in a thermal medium, like the quark gluon plasma. However, it is somehow mysterious the way that these phenomenological models work. In particular, what is the role of the fifth dimension and what is the relation between the holographic 5-d background and the physical (4-d) heavy mesons. Hadrons, in contrast to leptons, are composite particles with some internal structure, that depends on the energy at which they are observed. In this work, a static meson is represented by a heavy quark-antiquark pair with an interaction described by a Nambu Goto string living in the same 5-d background that provides field solutions leading to masses and decay constants of charmonium states. The interaction potential that shows up is linear for large distances with a string tension consistent with the effective Cornell potential. Introducing temperature $T$ in the background it is found, for the $J/\psi$ case, that there is a deconfining transition at some critical value of $T$. The results obtained indicate that the 5-d background is effectively representing the internal structure of the (static) charmonium (quasi) states.