Linear responses of D0-branes via gauge/gravity correspondence

Abstract

We study linear responses of D0-branes in the low frequency region by using gauge/gravity correspondence. The dynamics of the D0-branes is described by Matrix theory with finite temperature, which is dual to a near extremal D0-brane black hole solution. We analyze the tensor mode and vector modes of a stress tensor and a Ramond-Ramond 1-form current of Matrix theory. Then, we show that if a cutoff surface is close to a horizon of the D0-brane black hole, the linear responses take forms similar to the hydrodynamic stress tensor and current on S^8. By taking a Rindler limit, those linear responses come to obey the hydrodynamics exactly, which is consistent with previous works on a Rindler fluid. We also show that if the cutoff surface is far from the horizon, the linear responses do not take the forms of the hydrodynamic stress tensor and current on S^8. Especially, we find that the vector modes no longer possess a diffusion pole in the low frequency region, which indicates that the linear responses of the D0-branes cannot be explained by hydrodynamics.

40 pages, 1 figure; v2: references added and minor corrections; v3: minor corrections

References in corpus (8)

• Black holes as mirrors: quantum information in random subsystems
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Schwinger-Keldysh Propagators from AdS/CFT Correspondence
• Precision holography for non-conformal branes
• Addendum to Fast Scramblers
• Large N classical dynamics of holographic matrix models
• The Incompressible Rindler fluid versus the Schwarzschild-AdS fluid
• Shear viscosity of a highly excited string and the black hole membrane paradigm

Cited by in corpus (2)

• Matrix Thermalization
• D-dependence of gap between critical temperatures in one-dimensional gauge theories