14,534 research outputs found
Classical Aspects of Higher Spin Topologically Massive Gravity
We study the classical solutions of three dimensional topologically massive
gravity (TMG) and its higher spin generalization, in the first order
formulation. The action of higher spin TMG has been proposed in arXiv:1110.5113
to be of a Chern-Simons-like form. The equations of motion are more complicated
than the ones in pure higher spin AdS gravity, but are still tractable. As
all the solutions in higher spin gravity are automatically the solutions of
higher spin TMG, we focus on other solutions. We manage to find the AdS pp-wave
solutions with higher spin hair, and find that the nonvanishing higher spin
fields may or may not modify the pp-wave geometry. In order to discuss the
warped spacetime, we introduce the notion of special Killing vector, which is
defined to be the symmetry on the frame-like fields. We reproduce various
warped spacetimes of TMG in our framework, with the help of special Killing
vectors.Comment: 25 pages; minor corrections, references added, published versio
Holographic R\'enyi entropy for CFT with symmetry
In this paper we investigate the holographic R\'enyi entropy of two disjoint
intervals on complex plane with small cross ratio for conformal field
theory with symmetry in the ground state, which could be dual to a higher
spin AdS gravity. We focus on the cases of and symmetries. In
order to see the nontrivial contributions from the fields, we calculate the
R\'enyi entropy in the expansion of to order in both the gravity and
the CFT sides. In the gravity side the classical contributions to the
entanglement entropy is still given by the Ryu-Takayanagi area formula under
the reasonable assumption, while the 1-loop quantum corrections have to take
into account of the contributions not only from massless gravitons, but also
from massless higher spin fields. In the CFT side we still use the operator
product expansion of twist operators in the small interval limit, but now we
need to consider the quasiprimary fields constructed from fields, besides
the ones from Virasoro Verma module. In the large central charge limit, we
obtain the classical, 1-loop, 2-loop, and 3-loop parts of the R\'enyi entropy.
The classical and 1-loop results in the gravity and the CFT sides are in exact
match. This confirms the higher spin gravity/CFT correspondence, and also
supports the holographic computation of R\'enyi entanglement entropy, including
the quantum correction, in both the AdS gravity and the higher spin AdS
gravity.Comment: 32 pages, published versio
Hidden Conformal Symmetry of Extremal Black Holes
We study the hidden conformal symmetry of the extremal black holes. We
introduce a new set of conformal coordinates to write the generators.
We find that the Laplacian of the scalar field in many extremal black holes
could be written in terms of the quadratic Casimir. This suggests
that there exist dual CFT descriptions of these black holes. From the conformal
coordinates, the temperatures of the dual CFTs could be read directly. For the
extremal black hole, the Hawking temperature is vanishing. Correspondingly,
only the left (right) temperature of the dual CFT is non-vanishing and the
excitations of the other sector are suppressed. In the probe limit, we compute
the scattering amplitudes of the scalar off the extremal black holes and find
perfect agreement with the CFT prediction.Comment: 16 pages; Published versio
Dynamic Behaviors of Holling Type II Predator-Prey System with Mutual Interference and Impulses
A class of Holling type II predator-prey systems with mutual interference and impulses is presented. Sufficient conditions for the permanence, extinction, and global attractivity of system are obtained. The existence and uniqueness of positive periodic solution are also established. Numerical simulations are carried out to illustrate the theoretical results. Meanwhile, they indicate that dynamics of species are very sensitive with the period matching between species’ intrinsic disciplinarians and the perturbations from the variable environment. If the periods between individual growth and impulse perturbations match well, then the dynamics of species periodically change. If they mismatch each other, the dynamics differ from period to period until there is chaos
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