Holographic Operator Mixing and Quasinormal Modes on the Brane

TL;DR

This paper develops a framework for calculating holographic Green's functions in systems with coupled bulk fields, and applies it to analyze quasinormal modes and spectral functions in a D3/D7 brane setup at finite density.

Contribution

It introduces a general method for computing holographic Green's functions with coupled fields and applies it to study quasinormal modes in the D3/D7 system at finite density.

Findings

Spectral function is independent of the bulk radial coordinate.

Quasinormal modes transition from diffusive to reactive regimes with temperature and density.

Dispersion relations approach the lightcone at large momenta.

Abstract

We provide a framework for calculating holographic Green's functions from general bilinear actions and fields obeying coupled differential equations in the bulk. The matrix-valued spectral function is shown to be independent of the radial bulk coordinate. Applying this framework we improve the analysis of fluctuations in the D3/D7 system at finite baryon density, where the longitudinal perturbations of the world-volume gauge field couple to the scalar fluctuations of the brane embedding. We compute the spectral function and show how its properties are related to the quasinormal mode spectrum. We study the crossover from the hydrodynamic diffusive to the reactive regime and the movement of quasinormal modes as functions of temperature and density. We also compute their dispersion relations and find that they asymptote to the lightcone for large momenta.