An example of the convergence of hydrodynamics in strong external fields

The anti-de-Sitter/conformal field theory (AdS/CFT) correspondence is used to provide an estimate of the radius of convergence of the linearized gradient expansion of the hydrodynamic description of $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) theory minimally coupled to $U(1)$ gauge theory subjected to strong magnetic fields. The results of this work demonstrate that the dispersion relations of hydrodynamic modes continue to converge for magnetic field strengths far beyond those values for which a hydrodynamic description is expected. For magnetic field strengths much larger then the temperature scale the bulk dual interpolates between AdS$_{4+1}$ and the product of a Ba\~{n}ados-Teitelboim-Zanelli (BTZ) black hole and a two dimensional manifold (BTZ$_{2+1}\times \mathbb{R}^2$), and may be regarded as a renormalization group flow of the $3+1$ dimensional CFT to a $1+1$ dimensional CFT. In this regime, we clarify past literature on the quasi-normal mode (QNM) spectrum of bulk scalar fields by introducing a new way to classify the behavior of QNM collisions in the complex frequency and momentum plane.