1,965 research outputs found
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
Quadratically convergent multiple roots finding method without derivatives
AbstractIn this paper, an iteration method without derivatives for multiple roots is proposed. This method proved to be quadratically convergent. Its efficiency and accuracy are illustrated by numerical experiments
Non-Abelian Chiral Spin Liquid on the Kagome Lattice
We study spin liquid states on the kagome lattice constructed by
Gutzwiller-projected superconductors. We show that the obtained spin
liquids are either non-Abelian or Abelian topological phases, depending on the
topology of the fermionic mean-field state. By calculating the modular matrices
and , we confirm that projected topological superconductors are
non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin
Hall conductance we obtained agree very well with the (or,
equivalently, ) field theory predictions. We propose a local
Hamiltonian which may stabilize the NACSL. From a variational study we observe
a topological phase transition from the NACSL to the Abelian spin liquid.Comment: 12 pages, 7 figures, 1 tabl
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