Quasinormal modes and dispersion relations for quarkonium in a plasma

Recent investigations show that the thermal spectral function of heavy ${b \bar b }$ and ${c \bar c}$ vector mesons can be described using holography. These studies consider a bottom up model that captures the heavy flavour spectroscopy of masses and decay constants in the vacuum and is consistently extended to finite temperature. The corresponding spectral functions provide a picture of the dissociation process in terms of the decrease of the quasi-state peaks with temperature. Another related tool that provides important information about the thermal behaviour is the analysis of the quasinormal modes. They are field solutions in a curved background assumed to represent, in gauge/gravity duality, quasi-particle states in a thermal medium. The associated complex frequencies are related to the thermal mass and width. We present here the calculation of quasinormal modes for charmonium and bottomonium using the holographic approach. The temperature dependence of mass and thermal width are investigated. Solutions corresponding to heavy mesons moving into the plasma are also studied. They provide the dependence of the real and imaginary parts of the frequency with the quasi-particle momenta, the so called dispersion relations.Comment: V2: enlarged version with clarifications, more comparison with previous articles and additional references included. 11 figures, 2 tables, 62 references. Version accepted for publication in JHE

Anomalous dimensions from rotating open strings in AdS/CFT

We propose a new entry within the dictionary of the AdS/CFT duality at strong coupling: in the limit of a large spin or a large R-charge, the anomalous dimension of the gauge theory operator dual to a semiclassical rotating string is proportional to the string proper length. This conjecture is motivated by a generalization to strings of the rule for computing anomalous dimensions of massive particles and supergravity fields in the anti-de Sitter space. We show that this proportionality holds for a rotating closed string in global AdS space, representing a high spin operator made of fields in the adjoint representation. It is also valid for closed strings rotating in $S^5$ (representing operators with large R-charge), for closed strings with multiple AdS spin, and for giant magnons. Based on this conjecture, we calculate the anomalous dimension $\delta$ of operators made of fields in the fundamental representation, associated with high spin mesons, and which are represented by rotating open strings attached to probe D7-branes. The result is a logarithmic dependence upon the spin, $\delta\sim \sqrt{\lambda}\ln S$, similar to the closed string case. We show that the operator properties --- anomalous dimension and spin --- are obtained from measurements made by a local observer in the anti-de Sitter space. For the open string case, this ensures that these quantities are independent of the mass scale introduced by the D7-branes (the quark mass), as expected on physical grounds. In contrast, properties of the gauge theory states, like the energy, correspond to measurements by a gauge theory observer and depend upon the mass scale --- once again, as expected.Comment: V2: two related references include

Bottomonium dissociation in a finite density plasma

We present a holographic description of the thermal behavior of $b \bar b$ heavy vector mesons inside a plasma at finite temperature and density. The meson dissociation in the medium is represented by the decrease in the height of the spectral function peaks. In order to find a description for the evolution of the quasi-states with temperature and chemical potential it is crucial to use a model that is consistent with the decay constant behavior. The reason is that the height of a spectral function peak is related to the value of the zero temperature decay constant of the corresponding particle. AdS/QCD holographic models are in general not consistent with the observation that decay constants of heavy vector mesons decrease with radial excitation level. However, it was recently shown that using a soft wall background and calculating the correlation functions at a finite position of anti-de Sitter space, associated with an ultraviolet energy scale, it is possible to describe the observed behavior. Here we extend this proposal to the case of finite temperature $T$ and chemical potential $\mu$. A clear picture of the dissociation of bottomonium states as a function of $\mu$ and $T$ emerges from the spectral function. The energy scales where the change in chemical potential leads to changes in the thermal properties of the mesons is consistent with QCD expectations.Comment: In V3: errors in reference citations corrected. Version published in Physics Letters B. 15 pages, 3 figure