12,394 research outputs found
A Possible Hermitian Neutrino Mixing Ansatz
Using a recent global analysis result after the precise measurement of
, a possible Herimtian neutrino mixing ansatz is discussed, the
mixing matrix is symmetric and also symmetric with respect with the second
diagonal line in the leading order. This leading order ansatz predicts
. Next, consider the hierarchy structure of the lepton
mass matrix as the origin of perturbation of the mixing matrix, we find that
this ansatz with perturbation can fit current data very well.Comment: 13 pages, 4 figure
Holographic R\'enyi Entropy and Generalized Entropy method
In this paper we use the method of generalized gravitational entropy in
\cite{Lewkowycz:2013nqa} to construct the dual bulk geometry for a spherical
entangling surface, and calculate the R\'enyi entropy with the dual bulk
gravity theory being either Einstein gravity or Lovelock gravity, this approach
is closely related to that in \cite{Casini:2011kv}. For a general entangling
surface we derive the area law of entanglement entropy. The area law is closely
related with the local property of the entangling surface.Comment: 17+6 page
Entropy for gravitational Chern-Simons terms by squashed cone method
In this paper we investigate the entropy of gravitational Chern-Simons terms
for the horizon with non-vanishing extrinsic curvatures, or the holographic
entanglement entropy for arbitrary entangling surface. In 3D we find no anomaly
of entropy appears. But the squashed cone method can not be used directly to
get the correct result. For higher dimensions the anomaly of entropy would
appear, still, we can not use the squashed cone method directly. That is
becasuse the Chern-Simons action is not gauge invariant. To get a reasonable
result we suggest two methods. One is by adding a boundary term to recover the
gauge invariance. This boundary term can be derived from the variation of the
Chern-Simons action. The other one is by using the Chern-Simons relation
. We notice that the entropy of
is a total derivative locally, i.e. . We propose
to identify with the entropy of gravitational Chern-Simons terms
. In the first method we could get the correct result for Wald
entropy in arbitrary dimension. In the second approach, in addition to Wald
entropy, we can also obtain the anomaly of entropy with non-zero extrinsic
curvatures. Our results imply that the entropy of a topological invariant, such
as the Pontryagin term and the Euler density, is a
topological invariant on the entangling surface.Comment: 19 pag
Holographic Entanglement Entropy for the Most General Higher Derivative Gravity
The holographic entanglement entropy for the most general higher derivative
gravity is investigated. We find a new type of Wald entropy, which appears on
entangling surface without the rotational symmetry and reduces to usual Wald
entropy on Killing horizon. Furthermore, we obtain a formal formula of HEE for
the most general higher derivative gravity and work it out exactly for some
squashed cones. As an important application, we derive HEE for gravitational
action with one derivative of the curvature when the extrinsic curvature
vanishes. We also study some toy models with non-zero extrinsic curvature. We
prove that our formula yields the correct universal term of entanglement
entropy for 4d CFTs. Furthermore, we solve the puzzle raised by Hung, Myers and
Smolkin that the logarithmic term of entanglement entropy derived from Weyl
anomaly of CFTs does not match the holographic result even if the extrinsic
curvature vanishes. We find that such mismatch comes from the `anomaly of
entropy' of the derivative of curvature. After considering such contributions
carefully, we resolve the puzzle successfully. In general, we need to fix the
splitting problem for the conical metrics in order to derive the holographic
entanglement entropy. We find that, at least for Einstein gravity, the
splitting problem can be fixed by using equations of motion. How to derive the
splittings for higher derivative gravity is a non-trivial and open question.
For simplicity, we ignore the splitting problem in this paper and find that it
does not affect our main results.Comment: 28 pages, no figures, published in JHE
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