Duality in linearized gravity and holography

We consider spherical gravitational perturbations of AdS4 space-time satisfying general boundary conditions at spatial infinity. Using the holographic renormalization method, we compute the energy-momentum tensor and show that it can always be cast in the form of Cotton tensor for a dual boundary metric. In particular, axial and polar perturbations obeying the same boundary conditions for the effective Schrodinger wave-functions exhibit an energy-momentum/Cotton tensor duality at conformal infinity. We demonstrate explicitly that this is holographic manifestation of the electric/magnetic duality of linearized gravity in the bulk, which simply exchanges axial with polar perturbations of AdS4 space-time. We note on the side that this particular realization of gravitational duality is also valid for perturbations near flat and dS4 space-time, depending on the value of cosmological constant.Comment: 22 pages; a few clarifying remarks added at the end of section 6; missing factor sin^2 \theta inserted in eqs. (6.15) and (6.20) (version to be published in Class. Quant. Grav.

Dual photons and gravitons

We review the status of electric/magnetic duality for free gauge field theories in four space-time dimensions with emphasis on Maxwell theory and linearized Einstein gravity. Using the theory of vector and tensor spherical harmonics, we provide explicit construction of dual photons and gravitons by decomposing the fields into axial and polar configurations with opposite parity and interchanging the two sectors. When the theories are defined on AdS(4) space-time there are boundary manifestations of the duality, which for the case of gravity account for the energy-momentum/Cotton tensor duality (also known as dual graviton correspondence). For AdS(4) black-hole backgrounds there is no direct analogue of gravitational duality on the bulk, but there is still a boundary duality for quasi-normal modes satisfying a selected set of boundary conditions. Possible extensions of this framework and some open questions are also briefly discussed.Comment: 1+22 pages, conference proceeding

On the integrability of spherical gravitational waves in vacuum

The general class of Robinson-Trautman metrics that describe gravitational radiation in the exterior of bounded sources in four space-time dimensions is shown to admit zero curvature formulation in terms of appropriately chosen two-dimensional gauge connections. The result, which is valid for either type II or III metrics, implies that the gravitational analogue of the Lienard-Wiechert fields of Maxwell equations form a new integrable sector of Einstein equations for any value of the cosmological constant. The method of investigation is similar to that used for integrating the Ricci flow in two dimensions. The zero modes of the gauge symmetry (factored by the center) generate Kac's K_2 simple Lie algebra with infinite growth.Comment: 10 page

String Dualities and the Geroch Group

We examine the properties and symmetries of the lowest order effective theory of 4-dim string backgrounds with axion and dilaton fields and zero cosmological constant. The dimensional reduction yields an O(2,2) current group of transformations in the presence of two commuting Killing symmetries. Special emphasis is placed on the identification of the T and S string duality symmetries, and their intertwining relations. (Contributed to the Proceedings of the Satellite Colloquium "Topology, Strings and Integrable Models" to the XIth International Congress of Mathematical Physics, Paris, 25--28 July 1994; Diderot Editeur.)Comment: 3 pages, latex, no figure

Entanglement Entropy and Duality in AdS(4)

Small variations of the entanglement entropy \delta S and the expectation value of the modular Hamiltonian \delta E are computed holographically for circular entangling curves in the boundary of AdS(4), using gravitational perturbations with general boundary conditions in spherical coordinates. Agreement with the first law of thermodynamics, \delta S = \delta E, requires that the line element of the entangling curve remains constant. In this context, we also find a manifestation of electric-magnetic duality for the entanglement entropy and the corresponding modular Hamiltonian, following from the holographic energy-momentum/Cotton tensor duality.Comment: 43 pages, 2 figures, v2: a few clarifications have been added; final version to appear in Nucl. Phys.

T-duality, Quotients and Currents for Non-Geometric Closed Strings

We use the canonical description of T-duality as well as the formulation of T-duality in terms of chiral currents to investigate the geometric and non-geometric faces of closed string backgrounds originating from principal torus bundles with constant H-flux. Employing conformal field theory techniques, the non-commutative and non-associative structures among generalized coordinates in the so called Q-flux and R-flux backgrounds emerge by gauging the Abelian symmetries of an enlarged Rocek-Verlinde sigma-model and projecting the associated chiral currents of the enlarged theory to the T-dual coset models carrying non-geometric fluxes.Comment: 56 page

Non-equilibrium dynamics and AdS4AdS_4 Robinson-Trautman

The Robinson-Trautman space-times provide solutions of Einstein's equations with negative cosmological constant, which settle to $AdS_4$ Schwarzschild black hole at late times. Via gauge/gravity duality they should describe a system out of equilibrium that evolves towards thermalization. We show that the area of the past apparent horizon of these space-times satisfies a generalized Penrose inequality and we formulate as well as provide evidence for a suitable generalization of Thorne's hoop conjecture. We also compute the holographic energy-momentum tensor and deduce its late time behavior. It turns out that the complete non-equilibrium process on the boundary is governed by Calabi's flow on $S^2$. Upon linearization, only special modes that arise as supersymmetric zero energy states of an associated supersymmetric quantum mechanics problem contribute to the solution. We find that each pole of radiation has an effective viscosity given by the eigenvalues of the Laplace operator on $S^2$ and there is an apparent violation of the KSS bound on $\eta / s$ for the low lying harmonics of large $AdS_4$ black holes. These modes, however, do not satisfy Dirichlet boundary conditions, they are out-going and they do not appear to have a Kruskal extension across the future horizon ${\cal H}^+$.Comment: 48 pages, 2 figures, v2: new section on entropy current, refs added, JHEP versio

Homogeneous vacua of (generalized) new massive gravity

We obtain all homogeneous solutions of new massive gravity models on S^3 and AdS_3 by extending previously known results for the cosmological topologically massive theory of gravity in three dimensions. In all cases, apart from the maximally symmetric vacua, there are axially symmetric (i.e., bi-axially squashed) as well as totally anisotropic (i.e., tri-axially squashed) metrics of special algebraic type. Transitions among the vacua are modeled by instanton solutions of 3+1 Horava-Lifshitz gravity with anisotropic scaling parameter z=4.Comment: 1+25 pages; minor additions in conclusions (v2 to appear in Class. Quantum Grav.