arXiv subjects

P. Marios Petropoulos

Publications and source records attributed to P. Marios Petropoulos.

At least 37 records · Page 2Linked to original sources

arXiv2018

Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids

We provide the set of equations for non-relativistic fluid dynamics on arbitrary, possibly time-dependent spaces, in general coordinates. These equations are fully covariant under either local Galilean or local Carrollian transformations, and are obtained from standard relativistic hydrodynamics in the limit of infinite or vanishing velocity of light. All dissipative phenomena such as friction and heat conduction are included in our description. Part of our work consists in designing the appropriate coordinate frames for relativistic spacetimes, invariant under Galilean or Carrollian diffeomorphisms. The guide for the former is the dynamics of relativistic point particles, and leads to the Zermelo frame. For the latter, the relevant objects are relativistic instantonic space-filling branes in Randers-Papapetrou backgrounds. We apply our results for obtaining the general first-derivative-order Galilean fluid equations, in particular for incompressible fluids (Navier-Stokes equations) and further illustrate our findings with two applications: Galilean fluids in rotating frames or inflating surfaces and Carrollian conformal fluids on two-dimensional time-dependent geometries. The first is useful in atmospheric physics, while the dynamics emerging in the second is governed by the Robinson-Trautman equation, describing a Calabi flow on the surface, and known to appear when solving Einstein's equations for algebraically special Ricci-flat or Einstein spacetimes.

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arXiv2018

Petrov Classification and holographic reconstruction of spacetime

Using the asymptotic form of the bulk Weyl tensor, we present an explicit approach that allows us to reconstruct exact four-dimensional Einstein spacetimes which are algebraically special with respect to Petrov's classification. If the boundary metric supports a traceless, symmetric and conserved complex rank-two tensor, which is related to the boundary Cotton and energy-momentum tensors, and if the hydrodynamic congruence is shearless, then the bulk metric is exactly resummed and captures modes that stand beyond the hydrodynamic derivative expansion. We illustrate the method when the congruence has zero vorticity, leading to the Robinson-Trautman spacetimes of arbitrary Petrov class, and quote the case of non-vanishing vorticity, which captures the Plebanski-Demianski Petrov D family.

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arXiv2018

The Robinson-Trautman spacetime and its holographic fluid

We discuss the holographic reconstruction of four-dimensional asymptotically anti-de Sitter Robinson-Trautman spacetime from boundary data. We use for that a resummed version of the derivative expansion. The latter involves a vector field, which is interpreted as the dual-holographic-fluid velocity field and is naturally defined in the Eckart frame. In this frame the analysis of the non-perfect holographic energy-momentum tensor is considerably simplified. The Robinson-Trautman fluid is at rest and its time evolution is a heat-diffusion kind of phenomenon: the Robinson-Trautman equation plays the rôle of heat equation, and the heat current is identified with the gradient of the extrinsic curvature of the two-dimensional boundary spatial section hosting the conformal fluid, interpreted as an out-of-equilibrium kinematical temperature. The hydrodynamic-frame-independent entropy current is conserved for vanishing chemical potential, and the evolution of the fluid resembles a Moutier thermodynamic path. We finally comment on the general transformation rules for moving to the Landau-Lifshitz frame, and on possible drawbacks of this option.

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arXiv2017

Heisenberg symmetry and hypermultiplet manifolds

We study the emergence of Heisenberg (Bianchi II) algebra in hyper-Kähler and quaternionic spaces. This is motivated by the rôle these spaces with this symmetry play in $\mathcal{N}=2$ hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-Kähler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing cosmological constant. We further apply this method for the two hyper-Kähler spaces with Heisenberg algebra, which is reduced to $U(1)\times U(1)$ at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry -- as opposed to $\text{Heisenberg} \ltimes U(1)$. We finally discuss the realization of the latter by gauging appropriate $Sp(2,4)$ generators in $\mathcal{N}=2$ conformal supergravity.

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arXiv2016

Isometries, gaugings and N=2 supergravity decoupling

We study off-shell rigid limits for the kinetic and scalar-potential terms os a single N=2 hypermultiplet. In the kinetic term, these rigid limits establish relations between four-dimensional quaternion-Kahler and hyper-Kahler target spaces with symmetry. The scalar potential is obtained by gauging the graviphoton along an isometry of the quaternion-Kahler space. The rigid limits unveil two distinct cases. A rigid N=2 theory on Minkowski or on AdS_4 spacetime, depending on whether the isometry is translational or rotational respectively. We apply these results to the quaternion-Kahler space with Heisenberg x U(1) isometry, which describes the universal hypermultiplet at type-II string one-loop.

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arXiv2015

Geroch group for Einstein spaces and holographic integrability

We review how Geroch's reduction method is extended from Ricci-flat to Einstein spacetimes. The Ehlers-Geroch SL(2,R) group is still present in the three-dimensional sigma-model that captures the dynamics, but only a subgroup of it is solution-generating. Holography provides an alternative three-dimensional perspective to integrability properties of Einstein's equations in asymptotically anti-de Sitter spacetimes. These properties emerge as conditions on the boundary data (metric and energy-momentum tensor) ensuring that the hydrodynamic derivative expansion be resummed into an exact four-dimensional Einstein geometry. The conditions at hand are invariant under a set of transformations dubbed holographic U-duality group. The latter fills the gap left by the Ehlers-Geroch group in Einstein spaces, and allows for solution-generating maps mixing e.g. the mass and the nut charge.

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arXiv2015

Integrability, Einstein spaces and holographic fluids

Using holographic-fluid techniques, we discuss some aspects of the integrability properties of Einstein's equations in asymptotically anti-de Sitter spacetimes. We review and we amend the results of 1506.04813 on how exact four-dimensional Einstein spacetimes, which are algebraically special with respect to Petrov's classification, can be reconstructed from boundary data: this is possible if the boundary metric supports a traceless, symmetric and conserved complex rank-two tensor, which is related to the boundary Cotton and energy-momentum tensors, and if the hydrodynamic congruence is shearless. We illustrate the method when the hydrodynamic congruence has vorticity and the boundary metric has two commuting isometries. This leads to the complete Plebanski-Demianski family. The structure of the boundary consistency conditions depict a U(1) invariance for the boundary data, which is reminiscent of a Geroch-like solution-generating pattern for the bulk.

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arXiv2015

The Geroch group in Einstein spaces

Geroch's solution-generating method is extended to the case of Einstein spaces, which possess a Killing vector {{}and are thus asymptotically (locally) (anti-)de Sitter}. This includes the reduction to a three-dimensional coset space, the description of the dynamics in terms of a sigma-model and its transformation properties under the $SL(2,\mathbb{R})$ group, and the reconstruction of new four-dimensional Einstein spaces. The detailed analysis of the space of solutions is performed using the Hamilton--Jacobi method in the instance where the three-dimensional coset space is conformal to $\mathbb{R}\times \mathcal{S}_2$. The cosmological constant appears in this framework as a constant of motion and transforms under $SL(2,\mathbb{R})$.

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arXiv2014

Vorticity in holographic fluids

In view of the recent interest in reproducing holographically various properties of conformal fluids, we review the issue of vorticity in the context of AdS/CFT. Three-dimensional fluids with vorticity require four-dimensional bulk geometries with either angular momentum or nut charge, whose boundary geometries fall into the Papapetrou--Randers class. The boundary fluids emerge in stationary non-dissipative kinematic configurations, which can be cyclonic or vortex flows, evolving in compact or non-compact supports. A rich network of Einstein's solutions arises, naturally connected with three-dimensional Bianchi spaces. We use Fefferman--Graham expansion to handle holographic data from the bulk and discuss the alternative for reversing the process and reconstruct the exact bulk geometries.

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arXiv2014

Gravity duals of N=2 SCFTs and asymptotic emergence of the electrostatic description

We built the first eleven-dimensional supergravity solutions with SO(2,4)xSO(3)xU(1)_R symmetry that exhibit the asymptotic emergence of an extra U(1) isometry. This enables us to make the connection with the usual electrostatics-quiver description. The solution is obtained via the Toda frame of Kahler surfaces with vanishing scalar curvature and SU(2) action.

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arXiv2014

Gravitational duality, topologically massive gravity and holographic fluids

Self-duality in Euclidean gravitational set ups is a tool for finding remarkable geometries in four dimensions. From a holographic perspective, self-duality sets an algebraic 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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arXiv2014

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

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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arXiv2013

Gravity duals of N = 2 superconformal field theories with no electrostatic description

We construct the first eleven-dimensional supergravity solutions, which are regular, have no smearing and possess only SO(2,4) x SO(3) x U(1)_R isometry. They are dual to four-dimensional field theories with N = 2 superconformal symmetry. We utilise the Toda frame of self-dual four-dimensional Euclidean metrics with SU(2) rotational symmetry. They are obtained by transforming the Atiyah--Hitchin instanton under SL(2,R) and are expressed in terms of theta functions. The absence of any extra U(1) symmetry, even asymptotically, renders inapplicable the electrostatic description of our solution.

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arXiv2012

Gravity, strings, modular and quasimodular forms

Modular and quasimodular forms have played an important role in gravity and string theory. Eisenstein series have appeared systematically in the determination of spectrums and partition functions, in the description of non-perturbative effects, in higher-order corrections of scalar-field spaces, ... The latter often appear as gravitational instantons i.e. as special solutions of Einstein's equations. In the present lecture notes we present a class of such solutions in four dimensions, obtained by requiring (conformal) self-duality and Bianchi IX homogeneity. In this case, a vast range of configurations exist, which exhibit interesting modular properties. Examples of other Einstein spaces, without Bianchi IX symmetry, but with similar features are also given. Finally we discuss the emergence and the role of Eisenstein series in the framework of field and string theory perturbative expansions, and motivate the need for unravelling novel modular structures.

math-ph↗

arXiv2012

Holographic Fluids with Vorticity and Analogue Gravity

We study holographic three-dimensional fluids with vorticity in local equilibrium and discuss their relevance to analogue gravity systems. The Fefferman-Graham expansion leads to the fluid's description in terms of a comoving and rotating Papapetrou-Randers frame. A suitable Lorentz transformation brings the fluid to the non-inertial Zermelo frame, which clarifies its interpretation as moving media for light/sound propagation. We apply our general results to the Lorentzian Kerr-AdS_4 and Taub-NUT-AdS_4 geometries that describe fluids in cyclonic and vortex flows respectively. In the latter case we associate the appearance of closed timelike curves to analogue optical horizons. In addition, we derive the classical rotational Hall viscosity of three-dimensional fluids with vorticity. Our formula remarkably resembles the corresponding result in magnetized plasmas.

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arXiv2011

Holographic Three-Dimensional Fluids with Nontrivial Vorticity

Three-dimensional fluids with nontrivial vorticity can be described holographically. It is well-known that the Kerr-AdS geometry gives rise to a cyclonic flow. Here we note that Taub--NUT--AdS4 geometries give rise to a rotating fluid with vortex flow. The Randers and Zermelo forms of the boundary metrics provide alternative descriptions of the fluid by inertial co-moving or by accelerated observers. Such fluids possess acoustic horizons. Moreover, light propagation on the boundary Taub--NUT fluid will encounter an optical horizon associated with closed timelike curves. In the latter case the Misner string introduces a multi-valuedness of the scalar fluctuations which can be attributed to the anyonic nature of the boundary vortex.

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arXiv2009

Supersymmetric deformations of F1-NS5-branes and their exact CFT description

We consider certain classes of operators in the exact conformal field theory SL(2,R) x SU(2) x U(1)^4 describing strings in an AdS(3) x S(3) x T4 geometry supported by Neveu--Schwarz 3-form fluxes. This background arises in the near-horizon limit of a system of NS5-branes wrapped on a 4-torus and F1-branes smeared on the 4-torus when both types of branes are located at the same point in their common transverse space. We find a class of operators that lead to spacetime supersymmetric deformations. It is remarkable that most of these operators are not chiral primary with respect to the N=2 superconformal algebra on the wordsheet. A subset of these worldsheet conformal field theory deformations admits an interpretation either as a geometric deformation of the brane system or as a deformation of the distribution of the F1-branes, viewed as smooth instantons, inside the wrapped NS5-brane worldvolume. The 2-dimensional conformal field theory, however, seems to lack operators corresponding to arbitrary NS5-brane deformations, in contrast to pure NS5-brane systems where all geometric deformations can be accounted for by chiral primary operators.

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arXiv2008

Holographic approach to deformations of NS5-brane distributions and exact CFTs

We consider general planar deformations of a circular distribution of NS5-branes. The near-horizon region of the latter admits, after a T-duality transformation, an exact conformal-field-theory description in terms of the coset model SU(2)/U(1) X SL(2,R)/U(1). We derive the exactly marginal operators corresponding to an infinitesimal planar deformation using the conjectured holography between the coset model and the little string theory that resides on the worldvolume of the NS5-branes. Subsequently, we perform a complementary analysis of the same deformations using the associated N=1 supersymmetric sigma model and verify the holographic correspondence. We explicitly demonstrate a precise match between the two approaches which rests upon a delicate interplay between exact conformal-field-theory operators and their semiclassical realizations in terms of target-space variables.

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