arXiv subjects

Anastasios C. Petkou

Publications and source records attributed to Anastasios C. Petkou.

At least 37 records · Page 2Linked to original sources

arXiv2016

The free $σ$CFTs

We introduce the conformal field theories that describe the shadows of the lowest dimension composites made out of massless free scalars and fermions in $d$ dimensions. We argue that these theories can be consistently defined as free CFTs for even $d\geq 4$. We use OPE techniques to study their spectrum and show that for $d\rightarrow\infty$ it matches that of free bosonic CFTs in $d=6$ and $d=4$ dimensions. For these $σ$CFTs we calculate $c_T$ in $d=6,8,10$ and $12$ dimensions using the OPE and also a direct construction of their higher-derivative energy momentum tensors. Our results agree with the general proposal of arXiv:1601.07198.

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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

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

Singleton deformation of higher-spin theory and the phase structure of the three-dimensional O(N) vector model

We consider a singleton deformation of the AdS4 higher-spin theory dual to the three-dimensional O(N) vector model. The singleton couples to the higher-spin multiplet only through a marginal boundary interaction. We argue that the effect of such a deformation is to shift N to N+1 in both sides of the holographic correspondance and we show how the gap equations of the three-dimensional O(N) vector model arise from the higher-spin theory. The singleton deformation breaks higher-spin symmetry and gives rise to the well-known 1/N anomalous dimensions of the boundary theory.

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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

Instantons and the Hartle-Hawking-Maldacena Proposal for dS/CFT

We test the Maldacena proposal for the Hartle-Hawking late time quantum state in an asymptotically de Sitter universe. In particular, we calculate the on-shell action for scalar instantons on the southern hemisphere of the four-sphere and compare the result with the renormalized on-shell action for scalar instantons in EAdS$_4$. The two results agree provided the corresponding instanton moduli as well as the curvature radii are analytically continued. The instanton solutions in de Sitter are novel and satisfy mixed boundary conditions. We also point out that instantons on $S^4$ calculate the regularized volume of EAdS$_4$, while instantons on EAdS$_4$ calculate the volume of $S^4$, where the boundary condition of the instanton in one space is identified with the radius of curvature of the other. We briefly discuss the implications of the above geometric property of instantons for higher-spin holography.

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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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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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arXiv2010

Torsional degrees of freedom in AdS4/CFT3

We discuss the holographic implications of torsional degrees of freedom in the context of AdS4/CFT3, emphasizing in particular their physical interpretation as carriers of the non-trivial gravitational magnetic field, i.e. the part of the gravitational magnetic field not determined by the frame field. As a concrete example we present a new exact 4d gravitational background with torsion and argue that it corresponds to the holographic dual of a 3d system undergoing parity symmetry breaking. Finally, we compare our new gravitational background with known wormhole solutions - with and without cosmological constant - and argue that they can all be unified under an intriguing "Kalb-Ramond superconductivity" framework.

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arXiv2010

Gauge Fields, Membranes and Subdeterminant Vector Models

We present a class of classically marginal N-vector models in d=4 and d=3, whose scalar potentials can be written as subdeterminants of symmetric matrices. The d=3 case is a generalization of the scalar Bagger-Lambert-Gustavsson (BLG) model. Using the Hubbard-Stratonovich transformation we calculate their effective potentials which exhibit intriguing large-N scaling behaviors. We comment on the relevance of our models to strings, membranes and also to a class of novel spin systems that are based on ternary commutation relations.

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arXiv2009

Stochastic Quantization and AdS/CFT

We argue that there is a relationship between stochastic quantization and AdS/CFT, and we present an explicit calculation to support our claim. In particular, we show that a conformally coupled scalar with phi4 interaction on AdS4 is related, via stochastic quantization as well as via AdS/CFT, to a massless scalar with phi6 interaction in 3d. We show that our results have an underlying geometric origin, which might help to elucidate further the proposed relationship between stochastic quantization and holography.

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arXiv2008

Gravity in the 3+1-Split Formalism I: Holography as an Initial Value Problem

We present a detailed analysis of the 3+1-split formalism of gravity in the presence of a cosmological constant. The formalism helps revealing the intimate connection between holography and the initial value formulation of gravity. We show that the various methods of holographic subtraction of divergences correspond just to different transformations of the canonical variables, such that the initial value problem is properly set up at the boundary. The renormalized boundary energy momentum tensor is a component of the Weyl tensor.

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arXiv2008

Gravity in the 3+1-Split Formalism II: Self-Duality and the Emergence of the Gravitational Chern-Simons in the Boundary

We study self-duality in the context of the 3+1-split formalism of gravity with non-zero cosmological constant. Lorentzian self-dual configurations are conformally flat spacetimes and have boundary data determined by classical solutions of the three-dimensional gravitational Chern-Simons. For Euclidean self-dual configurations, the relationship between their boundary initial positions and initial velocity is also determined by the three-dimensional gravitational Chern-Simons. Our results imply that bulk self-dual configurations are holographically described by the gravitational Chern-Simons theory which can either viewed as a boundary generating functional or as a boundary effective action.

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arXiv2008

Torsion and the Gravity Dual of Parity Symmetry Breaking in AdS4/CFT3 Holography

We study four dimensional gravity with a negative cosmological constant deformed by the Nieh-Yan torsional topological invariant with a spacetime-dependent coefficient. We find an exact solution of the Euclidean system, which we call the torsion vortex, having two asymptotic AdS4 regimes supported by a pseudoscalar with a kink profile. We propose that the torsion vortex is the holographic dual of a three dimensional system that exhibits distinct parity breaking vacua. The torsion vortex represents a (holographic) transition between these distinct vacua. We expect that from the boundary point of view, the torsion vortex represents a `domain wall' between the two distinct vacua. From a bulk point of view, we point out an intriguing identification of the parameters of the torsion vortex with those of an Abrikosov vortex in a Type I superconductor. Following the analogy, we find that external Kalb-Ramond flux then appears to support bubbles of flat spacetime within an asymptotically AdS geometry.

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arXiv2008

An N=1 Superfield Action for M2 branes

We present an octonionic N=1 superfield action that reproduces in components the action of Bagger and Lambert for M2 branes. By giving an expectation value to one of the scalars we obtain the maximally supersymmetric superfield action for D2 branes.

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arXiv2007

Holographic Aspects of Electric-Magnetic Dualities

We review recent work on holographic aspects of electric-magnetic dualities in theories that involve conformally coupled scalars and abelian gauge fields in asymptotically AdS4 spaces. Such models are relevant for the holographic description of M-theory. We also briefly comment on some new results on the holographic properties of generalized electric-magnetic duality in gravity.

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arXiv2007

Gravitational Duality Transformations on (A)dS4

We discuss the implementation of electric-magnetic duality transformations in four-dimensional gravity linearized around Minkowski or (A)dS4 backgrounds. In the presence of a cosmological constant duality generically modifies the Hamiltonian, nevertheless the bulk dynamics is unchanged. We pay particular attention to the boundary terms generated by the duality transformations and discuss their implications for holography.

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