725 research outputs found
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.Comment: 25 pages; v2: minor improvements, references adde
Self-dual gravitational instantons and geometric flows of all Bianchi types
We investigate four-dimensional, self-dual gravitational instantons endowed
with a product structure RxM_3, where M_3 is homogeneous of Bianchi type. We
analyze the general conditions under which Euclidean-time evolution in the
gravitational instanton can be identified with a geometric flow of a metric on
M_3. This includes both unimodular and non-unimodular groups, and the
corresponding geometric flow is a general Ricci plus Yang-Mills flow
accompanied by a diffeomorphism.Comment: Latex, 12 pages; Final versio
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.Comment: 26 pages, 4 figures; v2: minor improvements, references adde
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.Comment: 28 pages; v2: minor improvements, references adde
Black hole entropy in 3D gravity with torsion
The role of torsion in quantum three-dimensional gravity is investigated by
studying the partition function of the Euclidean theory in Riemann-Cartan
spacetime. The entropy of the black hole with torsion is found to differ from
the standard Bekenstein-Hawking result, but its form is in complete agreement
with the first law of black hole thermodynamics.Comment: 17 pages, RevTeX, minor revision
Stochastic quantization and holographic Wilsonian renormalization group
We study relation between stochastic quantization and holographic Wilsonian
renormalization group flow. Considering stochastic quantization of the boundary
on-shell actions with the Dirichlet boundary condition for certain bulk
gravity theories, we find that the radial flows of double trace deformations in
the boundary effective actions are completely captured by stochastic time
evolution with identification of the radial coordinate `' with the
stochastic time '' as . More precisely, we investigate Langevin
dynamics and find an exact relation between radial flow of the double trace
couplings and 2-point correlation functions in stochastic quantization. We also
show that the radial evolution of double trace deformations in the boundary
effective action and the stochastic time evolution of the Fokker-Planck action
are the same. We demonstrate this relation with a couple of examples:
(minimally coupled)massless scalar fields in and U(1) vector fields in
.Comment: 1+30 pages, a new subsection is added, references are adde
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