Holographic spectral functions and diffusion constants for fundamental matter

TL;DR

This work uses the D3/D7 holographic setup to study finite‑temperature ${ m N}=2$ SYM with dynamical quarks in the high‑temperature phase where D7‑branes extend through the black hole horizon. By analyzing vector and scalar fluctuations of the D7 worldvolume fields, the authors compute spectral functions for flavor bilinears and extract the diffusion constant for fundamental matter using three independent holographic methods (membrane paradigm, Green–Kubo, and lowest quasinormal frequency). They show a first‑order meson melting transition separating a discrete, gapped spectrum in the low‑temperature phase from a continuous, largely featureless spectrum in the high‑temperature phase, with pronounced quasiparticle peaks appearing near the critical embedding and tachyonic instabilities signaling metastability. The results quantify how transport and spectral properties of fundamental quarks depend on temperature and quark mass, illustrating strong‑coupling dynamics relevant to hot QCD-like plasmas. Overall, the paper provides a coherent holographic characterization of meson dissolution, spectral structure, and quark diffusion in a controlled large‑N, strong‑coupling setting.

Abstract

The holographic dual of large-Nc super-Yang-Mills coupled to a small number of flavours of fundamental matter, Nf << Nc, is described by Nf probe D7-branes in the gravitational background of Nc black D3-branes. This system undergoes a first order phase transition characterised by the `melting' of the mesons. We study the high temperature phase in which the D7-branes extend through the black hole horizon. In this phase, we compute the spectral function for vector, scalar and pseudoscalar modes on the D7-brane probe. We also compute the diffusion constant for the flavour currents.