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...S4 [75, 76]. While all these discussions are for conformal fluids whose duals are asymptotically AdS spacetimes, one can extend the discussion to non-conformal fluids living on Dp-brane world-volumes =-=[77, 78]-=- as well as explorations involving higher derivative terms in the gravitational description [79]. Finally, the restriction of relativistic invariance can be relaxed to consider non-relativistic confor...

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... ∞ [14, 24]: lim λ→0 τπ η ∼ 5.9 ε + P , lim λ→∞ τπ ( ∼ 4 − 2 ln 2 + 375 8 ζ(3)λ−3/2 ) η ε + P . For non-conformal fluids, τΠ is known only in one particular example of a strongly coupled field theory =-=[25]-=- where ( 1 τΠ = τπ , ζ = 2η 3 − c2 ) η s , τπ = (4 − 2 ln2) ε + P . Remarkably, for these cases, the maximal propagation speeds (3.6) turn out to be less than unity, indicating that the second order f...

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...times that can be patched onto a domain wall solution?” This dualizes to the question, “what long-range behavior is possible for systems with merely Poincaré symmetry?” This approach was utilized in =-=[19]-=- in the context of hydrodynamics of nonconformal branes, for example, but we would like to continue to study phases of field theories to which DW/QFT applies. In a separate development, we recall that...

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... along a spacelike circle will result in a geometry which is conformally asymptotically locally anti-de Sitter in lower dimensions. This fact was used to analyze holography for nonconformal branes in =-=[42, 43]-=-. In the present case, reduction along the circle does not produce a geometry which is conformal to anti-de Sitter, and the reason is that the reduction being carried out is not along a spacelike circ...

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...f the bulk viscosity, the variable ( 1 3 − c2s ) can be used to parametrize deviations from conformality, and all transport coefficients can indeed be written explicitly as functions of ( 1 3 − c2s ) =-=[435]-=-. Let us conclude this section with a curious remark. As we saw in Section 2.2.3, the second order hydrodynamic equations are hyperbolic and, as such, they are causal. However, hydrodynamic equations ...

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... us briefly discuss some existing results regarding holography for non-AlAdS spacetimes. Many of these results are valid for spacetimes that are conformally related to AdS spacetimes, see for example =-=[17, 18, 19, 20, 21]-=- for geometries dual to non-conformal branes, or [22, 23] for results involving the cascading theories. See also [24] for a more abstract approach. Furthermore, several aspects of holography for Schro...

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...Maxwell fields and scalars, magnetic and dyonic charges, as well as more exotic models (see e.g. [16] for further references). Moreover, one can even extend the correspondence to non-conformal fluids =-=[53, 54]-=- as well as to non-relativistic fluids [55, 56], which allows us to make closer contact with familiar everyday systems. Nevertheless, many future directions and puzzles remain, as well the need for fu...

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... allowing one to continue this parameter to be any real number. In particular, this generalized reduction method was successfully applied to higher-dimensional AdS gravity coupled to matter fields in =-=[27]-=-, to obtain the holographic setup for lower-dimensional gravity coupled to a scalar field with exponential potential, which itself is associated with the near-horizon limit of non-conformal branes [25...