Hydrodynamics from the D1-brane

Abstract

We study the hydrodynamic properties of strongly coupled SU(N) Yang-Mills theory of the D1-brane at finite temperature in the framework of gauge/gravity duality. The only non-trivial viscous transport coefficient in 1 + 1 dimensions is the bulk viscosity. We evaluate the bulk viscosity by isolating the quasi-normal mode corresponding to the sound channel for the gravitational background of the D1-brane. We find that the ratio of the bulk viscosity to the entropy density to be 1/4π. This ratio continues to be 1/4π also in the regime when the D1brane Yang-Mills theory is dual to the gravitational background of the fundamental string. Our analysis shows that this ratio is equal to 1/4π for a class of gravitational backgrounds dual to field theories in 1 + 1 dimensions obtained by considering D1-branes at cones over Sasaki-Einstein 7-manifolds. * On lien from Harish-Chandra Research Institute, Allahabad.1 For a review and a complete list of references please see [8]

Second order transport coefficients of nonconformal relativistic fluids in various dimensions from Dp-brane

“…The above results agree with that of [37,46,48,50]. One can see from the sound speed that D5 and D6-brane are indeed unphysical since the sound speed separately become zero and negative for p = 5 and 6.…”

“…References of this kind are [13,16,37,[39][40][41][42][43][44][45][46][47][48][49][50][51], in which [39][40][41][42]47] are about the relativistic fluid that dual to supergravity backgrounds. And [13,16,37,[44][45][46][47][48][49][50][51] are about NS5-brane [44], Dp-brane [16,37,[46][47][48][49][50] and compactified D4-brane [13,45,51]. To be more specific, [37, 44-46, 48, 50, 51] study the first order transport coefficients while [13,16,47,49] investigate the second order ones, in which [16,…”

Adiabatic hydrodynamics: the eightfold way to dissipation

“…This then provides a possible avenue for ascertaining the non-equilibrium gravitational entropy current in time-dependent situations. 103 We noted in section 1 that often in addition to the second law of thermodynamics, one requires hydrodynamic transport to satisfy the Onsager relations [38,39]. This requirement is based for the most part on the empirical observation that most physical fluids satisfy these relations.…”

“…We note that [5,6,28,88] have studied specific aspects of transport in this particular set-up up to second order in gradients, but the full set of constitutive relations require turning on all possible background sources has yet to be done. Another direction to consider is neutral fluids without Weyl invariance, but since the simplest set-ups realizable holographically secretly enjoy higher dimensional conformal invariance [102] (see also [103,104]) it is easy to intuit that these analyses won't provide more detailed insight (see however [105] for explicit conformal symmetry breaking by sources). One could perhaps also make use of higher derivative gravitational theories, though in that case care must be exercised to ensure that one is dealing with a unitary QFT dual.…”

Fluid/gravity correspondence: A nonconformal realization in compactified D4 branes

“…Such studies include e.g. [65] for D1-brane and [66] for Dp-branes with p ≥ 2, where the Green-Kubo method is used. There is another interesting work on this topic which can handle more cases including p = 0, 1 and the fundamental strings in type II string theory (but p = 5 excluded): the Ref.…”