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.