109 research outputs found
4-dimensional Spin-foam Model with Quantum Lorentz Group
We study the quantum group deformation of the Lorentzian EPRL spin-foam
model. The construction uses the harmonic analysis on the quantum Lorentz
group. We show that the quantum group spin-foam model so defined is free of the
infra-red divergence, thus gives a finite partition function on a fixed
triangulation. We expect this quantum group spin-foam model is a spin-foam
quantization of discrete gravity with a cosmological constant.Comment: 23 pages, 3 figures, references adde
Canonical Path-Integral Measures for Holst and Plebanski Gravity. II. Gauge Invariance and Physical Inner Product
This article serves as a continuation for the discussion in arXiv:0911.3433,
we analyze the invariance properties of the gravity path-integral measure
derived from canonical framework, and discuss which path-integral formula may
be employed in the concrete computation e.g. constructing a spin-foam model, so
that the final model can be interpreted as a physical inner product in the
canonical theory.Comment: 34 page
Black Hole Entropy in Loop Quantum Gravity, Analytic Continuation, and Dual Holography
A new approach to black hole thermodynamics is proposed in Loop Quantum
Gravity (LQG), by defining a new black hole partition function, followed by
analytic continuations of Barbero-Immirzi parameter to
and Chern-Simons level to . The analytic continued partition
function has remarkable features: The black hole entropy is
reproduced correctly for infinitely many , at least for
. The near-horizon Unruh temperature emerges
as the pole of partition function. Interestingly, by analytic continuation the
partition function can have a dual statistical interpretation corresponding to
a dual quantum theory of . The dual quantum theory
implies a semiclassical area spectrum for . It also
implies that at a given near horizon (quantum) geometry, the number of quantum
states inside horizon is bounded by a holographic degeneracy , which produces the Bekenstein bound from LQG.
On the other hand, the result in arXiv:1212.4060 receives a justification
here.Comment: 5 pages, no figure
4d Quantum Geometry from 3d Supersymmetric Gauge Theory and Holomorphic Block
A class of 3d supersymmetric gauge theories are constructed
and shown to encode the simplicial geometries in 4-dimensions. The gauge
theories are defined by applying the Dimofte-Gaiotto-Gukov construction in
3d/3d correspondence to certain graph complement 3-manifolds. Given a gauge
theory in this class, the massive supersymmetric vacua of the theory contain
the classical geometries on a 4d simplicial complex. The corresponding 4d
simplicial geometries are locally constant curvature (either dS or AdS), in the
sense that they are made by gluing geometrical 4-simplices of the same constant
curvature. When the simplicial complex is sufficiently refined, the simplicial
geometries can approximate all possible smooth geometries on 4-manifold. At the
quantum level, we propose that a class of holomorphic blocks defined in
arXiv:1211.1986 from the 3d gauge theories are wave functions
of quantum 4d simplicial geometries. In the semiclassical limit, the asymptotic
behavior of holomorphic block reproduces the classical action of 4d
Einstein-Hilbert gravity in the simplicial context.Comment: 35+13 pages, 9 figures, presentation improved, reference adde
Covariant Loop Quantum Gravity, Low Energy Perturbation Theory, and Einstein Gravity with High Curvature UV Corrections
A low-energy perturbation theory is developed from the nonperturbative
framework of covariant Loop Quantum Gravity (LQG) by employing the background
field method. The resulting perturbation theory is a 2-parameter expansion in
the semiclassical and low-energy regime. The two expansion parameters are the
large spin and small curvature. The leading order effective action coincides
with the Einstein-Hilbert action. The subleading corrections organized by the
two expansion parameters give the modifications of Einstein gravity in quantum
and high-energy regime from LQG. The perturbation theory developed here shows
for the first time that covariant LQG produces the high curvature corrections
to Einstein gravity. This result means that LQG is not a naive quantization of
Einstein gravity, but rather provides the UV modification. The result of the
paper may be viewed as the first step toward understanding the UV completeness
of LQG.Comment: 5 pages, 1 figure, presentation improved, references adde
Semiclassical Analysis of Spinfoam Model with a Small Barbero-Immirzi Parameter
We study the semiclassical behavior of Lorentzian
Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model, by taking into account of
the sum over spins in the large spin regime. The large spin parameter \lambda
and small Barbero-Immirzi parameter \gamma are treated as two independent
parameters for the asymptotic expansion of spinfoam state-sum (such an idea was
firstly pointed out in arXiv:1105.0216). Interestingly, there are two different
spin regimes: 1\gamma^{-2}. The
model in two spin regimes has dramatically different number of effective
degrees of freedom. In 1<<\gamma^{-1}<<\lambda<<\gamma^{-2}, the model produces
in the leading order a functional integration of Regge action, which gives the
discrete Einstein equation for the leading contribution. There is no
restriction of Lorentzian deficit angle in this regime. In the other regime
\lambda>\gamma^{-2}, only small deficit angle is allowed
|\Theta_f|<<\gamma^{-1}\lambda^{1/2}$ mod 4\pi Z. When spins go even larger,
only zero deficit angle mod 4\pi Z is allowed asymptotically. In the transition
of the two regimes, only the configurations with small deficit angle can
contribute, which means one need a large triangulation in order to have
oscillatory behavior of the spinfoam amplitude.Comment: 21 pages, 2 figure
Discrete Gravity on Random Tensor Network and Holographic R\'enyi Entropy
In this paper we apply the discrete gravity and Regge calculus to tensor
networks and Anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We
construct the boundary many-body quantum state using random
tensor networks as the holographic mapping, applied to the Wheeler-deWitt wave
function of bulk Euclidean discrete gravity in 3 dimensions. The entanglement
R\'enyi entropy of is shown to holographically relate to the
on-shell action of Einstein gravity on a branch cover bulk manifold. The
resulting R\'enyi entropy of approximates with high
precision the R\'enyi entropy of ground state in 2-dimensional conformal field
theory (CFT). In particular it reproduces the correct dependence. Our
results develop the framework of realizing the AdS/CFT correspondence
on random tensor networks, and provide a new proposal to approximate CFT ground
state.Comment: 8+2 pages, 10 figures, presentation improved, references adde
Generalized Spinfoams
We reconsider the spinfoam dynamics that has been recently introduced, in the
generalized Kaminski-Kisielowski-Lewandowski (KKL) version where the foam is
not dual to a triangulation. We study the Euclidean as well as the Lorentzian
case. We show that this theory can still be obtained as a constrained BF theory
satisfying the simplicity constraint, now discretized on a general oriented
2-cell complex. This constraint implies that boundary states admit a (quantum)
geometrical interpretation in terms of polyhedra, generalizing the tetrahedral
geometry of the simplicial case. We also point out that the general solution to
this constraint (imposed weakly) depends on a quantum number r_f in addition to
those of loop quantum gravity. We compute the vertex amplitude and recover the
KKL amplitude in the Euclidean theory when r_f=0. We comment on the eventual
physical relevance of r_f, and the formal way to eliminate it.Comment: 16 pages, 3 figure
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