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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="script">N</a:mi><a:mo>=</a:mo><a:mn>4</a:mn></a:math> supersymmetric Yang-Mills (SYM) theory minimally coupled to <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>U</d:mi><d:mo stretchy="false">(</d:mo><d:mn>1</d:mn><d:mo stretchy="false">)</d:mo></d:math> 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 <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mrow><h:msub><h:mrow><h:mi>AdS</h:mi></h:mrow><h:mrow><h:mn>4</h:mn><h:mo>+</h:mo><h:mn>1</h:mn></h:mrow></h:msub></h:mrow></h:math> and the product of a Bañados-Teitelboim-Zanelli (BTZ) black hole and a two dimensional manifold (<j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mrow><j:msub><j:mrow><j:mi>BTZ</j:mi></j:mrow><j:mrow><j:mn>2</j:mn><j:mo>+</j:mo><j:mn>1</j:mn></j:mrow></j:msub><j:mo>×</j:mo><j:msup><j:mi mathvariant="double-struck">R</j:mi><j:mn>2</j:mn></j:msup></j:mrow></j:math>) and may be regarded as a renormalization group flow of the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mn>3</m:mn><m:mo>+</m:mo><m:mn>1</m:mn></m:math> dimensional CFT to a <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mn>1</o:mn><o:mo>+</o:mo><o:mn>1</o:mn></o:math> 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. Published by the American Physical Society 2024