Fluid/gravity correspondence: second order transport coefficients in compactified D4-branes

We study second-order hydrodynamic transport in strongly coupled non-conformal field theories with holographic gravity duals in asymptotically anti-de Sitter space. We first derive new Kubo formulae for five second-order transport coefficients in nonconformal fluids in (3 + 1) dimensions. We then apply them to holographic RG flows induced by scalar operators of dimension ∆ = 3. For general background solutions of the dual bulk geometry, we find explicit expressions for the five transport coefficients at infinite coupling and show that a specific combination,H = 2ητ π − 2 (κ − κ * ) − λ 2 , always vanishes. We prove analytically that the Haack-Yarom identity H = 2ητ π − 4λ 1 − λ 2 = 0, which is known to be true for conformal holographic fluids at infinite coupling, also holds when taking into account leading non-conformal corrections. The numerical results we obtain for two specific families of RG flows suggest that H vanishes regardless of conformal symmetry. Our work provides further evidence that the Haack-Yarom identity H = 0 may be universally satisfied by strongly coupled fluids.

“…These relations are indeed satisfied in the examples of compactified backgrounds for which first-and second-order transport has been studied [50,107].…”

Section: Jhep12(2016)091mentioning

confidence: 70%

Section: Jhep12(2016)091mentioning

confidence: 77%

Section: Jhep12(2016)091 7 Conclusion and Outlookmentioning

confidence: 80%

“…[47] nor the compactified branes of ref. [50] admit an asymptotically AdS region. 2 Their holographic duals therefore do not have an obvious UV fixed point.…”

Section: Jhep12(2016)091mentioning

confidence: 99%

Section: Jhep12(2016)091mentioning

confidence: 99%

See 3 more Smart Citations

Second-order hydrodynamics and universality in non-conformal holographic fluids

Kleinert

Probst

2016

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

2019

Self Cite

We derive all the dynamical second order transport coefficients for Dpbrane with p from 1 to 6 within the framework of fluid/gravity correspondence in this paper. The D5 and D6-brane do not have dual relativistic fluids; D3-brane corresponds to 4-dimensional conformal relativistic fluid; D1, D2 and D4-brane separately correspond to nonconformal relativistic fluids of dimensions 2, 3 and 5. The Haack-Yarom relation only exists for Dp-branes with p larger than 2 and is also satisfied by them. We also find that the Romatschke and Kleinert-Probst relations need to be generalized in order to be valid for relativistic fluids of dimensions other than 4.

Compactified AdS black holes, Chamblin-Reall background, and their dual non-conformal relativistic fluids

Wu¹,

Wang²

2022

Self Cite

The Chamblin-Reall background is a static solution of Einstein gravity coupled with a background scalar field and a dynamical domain wall, with the potential of the scalar field being of Liouville type. It can be got by dimensionally reducing a higher dimensional background with a constant potential. Compactified AdS black holes are black hole backgrounds constructed by wrapping one or more spatial directions of a higher dimensional AdS black hole on a torus and then integrating them out. The compactified AdS black hole background is asymptotically flat, non-conformal, and of Chamblin-Reall type. In this work, we derive all the 7 dynamical second-order transport coefficients for the relativistic fluids dual to compactified AdS black holes of various dimensions via fluid/gravity correspondence. Through this work, we achieve three main goals: (1) We prove that all the gravitational backgrounds that can be used to extract analytical results for second-order transport coefficients hitherto are all Chamblin-Reall type backgrounds. (2) We generalize the results in previous studies on the second-order transport coefficients of the relativistic fluids dual to 5-dimensional Chamblin-Reall model into general dimensions. (3) We offer a thorough study on the Kanitscheider-Skenderis proposal and find its physical accounts.