Structure function of holographic quark-gluon plasma: Sakai-Sugimoto model versus its non-critical version

Motivated by recent studies of deep inelastic scattering (DIS) off the $\mathcal{N}=4$ super-Yang-Mills (SYM) plasma, holographically dual to $AdS_5\times S^5$ black hole, we in this note use the spacelike flavor current to probe the internal structure of one holographic quark-gluon plasma, which is described by the Sakai-Sugimoto model at high temperature phase (i.e., the chiral symmetric phase). The plasma structure function is extracted from the retarded flavor current-current correlator. Our main aim here is to explore the effect of non-conformality on these physical quantities. As usual, our study is under the supergravity approximation and the limit of large color number. Although the Sakai-Sugimoto model is non-conformal, which makes the calculations more involved than the well-studied $\mathcal {N}$=4 SYM case, the result seems to indicate that the non-conformality has little essential effect on the physical picture of the internal structure of holographic plasma, which is consistent with the intuition from the asymptotic freedom of QCD at high energy. While the physical picture underlying our investigation is same as the DIS off the $\mathcal {N}$=4 SYM plasma with(out) flavor, the plasma structure functions are quantitatively different, especially their scaling dependence on the temperature, which can be recognized as model-dependent. As a comparison, we also do the same analysis for the non-critical version of the Sakai-Sugimoto model which is conformal in the sense that it has a constant dilaton vacuum. The result for this non-critical model is much similar to the conformal $\mathcal{N}=4$ SYM plasma. We therefore attribute the above difference to the effect of non-conformality of the Sakai-Sugimoto model.Comment: 22 pages, no figure, Version accepted by Physical Review

Spectral function and quark diffusion constant in non-critical holographic QCD

Motivated by recent studies of intersecting D-brane systems in critical string theory and phenomenological AdS/QCD models, we present a detailed analysis for the vector and scalar fluctuations in a non-critical holographic QCD model in the high temperature phase, i.e., the chiral symmetric phase. This model is described by $N_f$ pairs of D4 and $\bar{\text{D4}}$ probe branes in a non-critical ${AdS_6}$ black hole background. Focusing on the hydrodynamic as well as the high frequency limit, we analytically obtain spectral functions for vector and scalar modes on the flavor probe. Then we extract the light quark diffusion constant for flavor current using three different methods and find that different methods give the same results. We also compute the heavy quark diffusion constant for comparison with the light quark case.Comment: 37 pages, no figures; Version to be published in Nuclear Physics

Extension Of Bertrand's Theorem And Factorization Of The Radial Schr\"odinger Equation

The Bertrand's theorem is extended, i.e. closed orbits still may exist for other central potentials than the power law Coulomb potential and isotropic harmonic oscillator. It is shown that for the combined potential $V(r)=W(r)+b/r^2$ ($W(r)=ar^{\nu}$), when (and only when) $W(r)$ is the Coulomb potential or isotropic harmonic oscillator, closed orbits still exist for suitable angular momentum. The correspondence between the closeness of classical orbits and the existence of raising and lowering operators derived from the factorization of the radial Schr\"odinger equation is investigated.Comment: 4 pages, 1 figug