4,310 research outputs found
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
Geometric flows and (some of) their physical applications
The geometric evolution equations provide new ways to address a variety of
non-linear problems in Riemannian geometry, and, at the same time, they enjoy
numerous physical applications, most notably within the renormalization group
analysis of non-linear sigma models and in general relativity. They are divided
into classes of intrinsic and extrinsic curvature flows. Here, we review the
main aspects of intrinsic geometric flows driven by the Ricci curvature, in
various forms, and explain the intimate relation between Ricci and Calabi flows
on Kahler manifolds using the notion of super-evolution. The integration of
these flows on two-dimensional surfaces relies on the introduction of a novel
class of infinite dimensional algebras with infinite growth. It is also
explained in this context how Kac's K_2 simple Lie algebra can be used to
construct metrics on S^2 with prescribed scalar curvature equal to the sum of
any holomorphic function and its complex conjugate; applications of this
special problem to general relativity and to a model of interfaces in
statistical mechanics are also briefly discussed.Comment: 18 pages, contribution to AvH conference Advances in Physics and
Astrophysics of the 21st Century, 6-11 September 2005, Varna, Bulgari
Conservation Laws and Geometry of Perturbed Coset Models
We present a Lagrangian description of the coset model perturbed
by its first thermal operator. This is the simplest perturbation that changes
sign under Krammers--Wannier duality. The resulting theory, which is a
2--component generalization of the sine--Gordon model, is then taken in
Minkowski space. For negative values of the coupling constant , it is
classically equivalent to the non--linear \s--model reduced in a
certain frame. For , it describes the relativistic motion of vortices in
a constant external field. Viewing the classical equations of motion as a zero
curvature condition, we obtain recursive relations for the infinitely many
conservation laws by the abelianization method of gauge connections. The higher
spin currents are constructed entirely using an off--critical generalization of
the generators. We give a geometric interpretation to the
corresponding charges in terms of embeddings. Applications to the chirally
invariant Gross--Neveu model are also discussed.Comment: Latex, 31p, CERN-TH.7047/9
O(2,2) Transformations and the String Geroch Group
The 1--loop string background equations with axion and dilaton fields are
shown to be integrable in four dimensions in the presence of two commuting
Killing symmetries and . Then, in analogy with reduced gravity,
there is an infinite group that acts on the space of solutions and generates
non--trivial string backgrounds from flat space. The usual and
--duality transformations are just special cases of the string Geroch group,
which is infinitesimally identified with the current algebra. We also
find an additional symmetry interchanging the field content of the
dimensionally reduced string equations. The method for constructing
multi--soliton solutions on a given string background is briefly discussed.Comment: Latex, 26p., CERN-TH.7144/9
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
Destroying Angel
Poetry by Karena Bakas. Runner-Up in the 2017 Manuscripts Poetry Contest with Alessandra Lynch
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