Yoshinori Matsuo, Yuya Sasai, Yasuhiro Sekino
We study linear responses of D0-branes in 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 tensor mode and vector modes of a stress tensor and a Ramond-Ramond (R-R) 1-form current of Matrix theory. Then, we show that if a cut-off 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 become to obey the hydrodynamics exactly, which is consistent with previous works on a Rindler fluid. We also show that if the cut-off 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 low frequency region, which indicates that the linear responses of the D0-branes can not be explained by hydrodynamics.
View original:
http://arxiv.org/abs/1305.2506
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