Holographic three-dimensional fluids with nontrivial vorticity

Leigh, Robert G.; Petkou, Anastasios C.; Petropoulos, P. Marios

doi:10.1103/physrevd.85.086010

Cited by 29 publications

(53 citation statements)

References 40 publications

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“…Non-cyclonic vorticity on the boundary requires precisely non-zero Cotton, as we discuss in section 4. This was unambiguously stated in [20][21][22] in relation with the nut charge, the latter being encapsulated in the Weyl component Ψ2 (see Griffiths and Podolský p. 215 [37], and for applications in fluid/gravity correspondence [38]). Clearly, the structure of the perfect Cotton puts constraints on the bulk Weyl tensor.…”

Section: Generic Bulk Reconstructionmentioning

confidence: 69%

“…These metrics were introduced by Papapetrou in [17]. They will be called hereafter Papapetrou-Randers because they are part of an interesting network of relationships involving the Randers form [18], discussed in detail in [19] and more recently used in [20][21][22].…”

Section: Fluids In Papapetrou-randers Geometriesmentioning

confidence: 99%

“…20 It was shown to be exact for the Taub-NUT boundary in [22] -as well as for Kerr whose boundary has vanishing Cotton. Metric (5.10) coincides precisely with (5.3) for perfect-Cotton boundary geometries.…”

Section: Jhep04(2014)136mentioning

confidence: 99%

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Holographic perfect fluidity, Cotton energy-momentum duality and transport properties

Mukhopadhyay

Petkou

Petropoulos

et al. 2014

J. High Energ. Phys.

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We investigate background metrics for 2 + 1-dimensional holographic theories where the equilibrium solution behaves as a perfect fluid, and admits thus a thermodynamic description. We introduce stationary perfect-Cotton geometries, where the Cotton-York tensor takes the form of the energy-momentum tensor of a perfect fluid, i.e. they are of Petrov type D t . Fluids in equilibrium in such boundary geometries have non-trivial vorticity. The corresponding bulk can be exactly reconstructed to obtain 3 + 1-dimensional stationary black-hole solutions with no naked singularities for appropriate values of the black-hole mass. It follows that an infinite number of transport coefficients vanish for holographic fluids. Our results imply an intimate relationship between black-hole uniqueness and holographic perfect equilibrium. They also point towards a Cotton/energy-momentum tensor duality constraining the fluid vorticity, as an intriguing boundary manifestation of the bulk mass/nut duality.

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Section: Generic Bulk Reconstructionmentioning

confidence: 69%

Section: Fluids In Papapetrou-randers Geometriesmentioning

confidence: 99%

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Holographic perfect fluidity, Cotton energy-momentum duality and transport properties

Mukhopadhyay

Petkou

Petropoulos

et al. 2014

J. High Energ. Phys.

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“…Such NFL behaviour indeed bears some superficial resemblance to that found in a certain class of the heavy-fermion compounds [45] and DMFT calculations [46]. However, it is also plagued with such spurious features as potentially multiple Fermi surfaces, dispersionless peaks, and log-oscillating ω-dependence [35][36][37][38][39][40][41][42][43][44].…”

Section: Condensed Matter Holography: the Evidencementioning

confidence: 54%

“…This behaviour makes them potentially amenable to the description based on the holographic 'semi-locally critical' scenario of Refs. [35][36][37][38][39][40][41][42][43][44].…”

Section: Emergent Geometry and 'Holography Light'mentioning

confidence: 99%

Demystifying the holographic mystique: A critical review

Khveshchenko¹

2016

Lith. J. Phys.

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Thus far, in spite of many interesting developments, the overall progress towards a systematic study and classification of various 'strange' metallic states of matter has been rather limited. To that end, it was argued that a recent proliferation of the ideas of holographic correspondence originating from string theory might offer a possible way out of the stalemate. However, after almost a decade of intensive studies into the proposed extensions of the holographic conjecture to a variety of condensed matter problems, the validity of this intriguing approach remains largely unknown. This discussion aims at ascertaining its true status and elucidating the conditions under which some of its predictions may indeed be right (albeit, possibly, for a wrong reason).Keywords: strongly correlated systems, holographic correspondence, transport theory, strange metals, analogue gravity PACS: 71.27.+a Condensed matter holography: the promiseAmong the outstanding grand problems in condensed matter physics is that of a deeper understanding and classification of the so-called 'strange metals' or compressible non-Fermi liquid (NFL) states of the strongly interacting systems. However, despite all the effort and a plethora of the important and nontrivial results obtained with the use of the traditional techniques, this program still remains far from completion.As an alternate approach, over the past decade there have been numerous attempts inspired by the hypothetical idea of holographic correspondence which originated from string/gravity/high energy theory (where it is known under the acronym AdS/ CFT) to adapt its main concepts to various condensed matter (or, even more generally, quantum manybody) systems at finite densities and temperatures [1][2][3][4][5][6][7].In its original context, the bona fide holographic principle postulates that certain d + 1-dimensional ('boundary') quantum field theories (e. g. the maximally supersymmetric SU(N) gauge theory) may allow for a dual description in terms of a string theory which, upon a proper compactification, amounts to a certain d + 2-dimensional ('bulk') supergravity. Moreover, in the strong coupling limit (characterized in terms of the t'Hooft coupling constant λ = g 2 N >> 1) and for a large rank N > > 1 of the gauge symmetry group, the bulk description can be further reduced down to a weakly fluctuating gravity model which can even be treated semiclassically at the lowest (0th) order of the underlying 1/N-expansion.In the practical applications of the holographic conjecture, the partition function of a strongly interacting boundary theory with the Lagrangian L(ϕ a ) would then be approximated by a saddle-point (classical) value of the bulk action described by the Lagrangian L(g μν ,…) which includes gravity and other fields dual to their boundary counterparts [1][2][3][4][5][6][7][8] (1) evaluated with the use of a fixed background metric ,while any quantum corrections would usually be neglected by invoking the small parameter 1/N.

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Gravitational Duality, Topologically Massive Gravity and Holographic Fluids

Petropoulos

2014

Modifications of Einstein's Theory of Gravity at Large Distances

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Self-duality in Euclidean gravitational set ups is a tool for finding remarkable four-dimensional geometries. From a holographic perspective, selfduality sets a relationship between two a priori independent boundary data: the boundary energy-momentum tensor and the boundary Cotton tensor. This relationship, which can be viewed as resulting from a topological mass term for gravity boundary dynamics, survives under the Lorentzian signature and provides a tool for generating exact bulk Einstein spaces carrying, among others, nut charge. In turn, the holographic analysis exhibits perfect-fluid-like equilibrium states and the presence of non-trivial vorticity allows to show that infinite number of transport coefficients vanish.

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Holographic three-dimensional fluids with nontrivial vorticity

Cited by 29 publications

References 40 publications

Holographic perfect fluidity, Cotton energy-momentum duality and transport properties

Holographic perfect fluidity, Cotton energy-momentum duality and transport properties

Demystifying the holographic mystique: A critical review

Gravitational Duality, Topologically Massive Gravity and Holographic Fluids

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