Holographic melting and related properties of mesons in a quark gluon plasma

TL;DR

The paper analyzes mesons in a holographic QCD setting (Sakai-Sugimoto) at finite temperature across three phases: confining, deconfined with broken chiral symmetry, and deconfined with restored chiral symmetry. Using fluctuations on the probe branes and rotating string configurations, it finds lattice-like temperature trends for low-spin mesons, a spin-dependent melting for high-spin mesons, and no drag for rotating large-spin mesons, with a velocity-dependent melting threshold. It further shows that in the high-temperature phase the Goldstone boson disappears and the spectrum becomes continuous, reflecting chiral symmetry restoration and deconfinement of the flavor sector. Overall, the results qualitatively align with lattice and heavy-quark phenomenology, while providing concrete holographic predictions for meson dissociation and drag behavior in a thermal QCD-like plasma.

Abstract

We analyse mesons at finite temperature in a chiral, confining string dual. The temperature dependence of low-spin as well as high-spin meson masses is shown to exhibit a pattern familiar from the lattice. Furthermore, we find the dissociation temperature of mesons as a function of their spin, showing that at a fixed quark mass, mesons with larger spins dissociate at lower temperatures. The Goldstone bosons associated with chiral symmetry breaking are shown to disappear above the chiral symmetry restoration temperature. Finally, we show that holographic consideration imply that large-spin mesons do not experience drag effects when moving through the quark gluon plasma. They do, however, have a maximum velocity for fixed spin, beyond which they dissociate.

Figures (16)

• Figure 1: The Sakai & Sugimoto model in the low-temperature (left panel), intermediate-temperature (middle panel) and high-temperature (right panel) phases. Depicted are the two compact Euclidean directions $x^4$ (the Kaluza-Klein circle) and $t$ (Wick rotated time). The D8 embedding is shown as well (in blue).
• Figure 2: The asymptotic distance $L$ between the D8 and anti-D8 as a function of $y_T := u_T/u_0$. The red dashed line indicates the phase transition to the high-temperature phase, above which one should instead use two parallel D8 stacks. Note that "$L = \text{const.} \rightarrow u_0 = \text{const.}$" holds to good approximation in the intermediate-temperature regime.
• Figure 3: Meson masses (squared) as a function of level $n$ for the zero temperature (upper dots) and intermediate-temperature phases (lower dots), for an asymptotic separation between the D8 and anti-D8 fixed at $L/R=0.63$, with $u_\Lambda=u_T=1$. (Extensions of these curves to even higher level show $m^2 \sim n^2$ behaviour for large $n$, both at zero and at finite temperature, which is one of the unrealistic features of these models Schreiber:2004ieShifman:2005znKarch:2006pv).
• Figure 4: Squared masses of the two lightest vector mesons as a function of temperature in the intermediate-temperature regime, for $L=0.256 < 0.97\, R$. Masses are normalised as in \ref{['midT']}. The decrease of the mass is in qualitative agreement with results from other models and experiments Shuryak:2003xe, though one should be cautious since the latter are not in the large-$N_c$ limit. The $\rho$ and $a_1$ do not become degenerate in our model.
• Figure 5: Behaviour of six lowest-mass vector mesons (for fixed $L/R$) as a function of temperature in the intermediate-temperature regime, and a comparison with the masses in the low-temperature phase. Note the jump in the spectrum at the confinement/deconfinement transition, and also note that the masses of the higher excited modes do not exhibit monotonic behaviour as a function of temperature.