19,773 research outputs found
c-theorem of the entanglement entropy
We holographically investigate the renormalization group flow in a
two-dimensional conformal field theory deformed by a relevant operator. If the
relevant operator allows another fixed point, the UV conformal field theory
smoothly flows to a new IR conformal field theory. From the holographic point
of view, such a renormalization group flow can be realized as a dual geometry
interpolating two different AdS boundaries. On this interpolating geometry, we
investigate how the c-function of the entanglement entropy behaves along the RG
flow analyt- ically and numerically, which reproduces the expected central
charges of UV and IR. We also show that the c-function monotonically decreases
from UV to IR without any phase transition.Comment: 24 pages, 8 figure
Mutual information and the F-theorem
Mutual information is used as a purely geometrical regularization of
entanglement entropy applicable to any QFT. A coefficient in the mutual
information between concentric circular entangling surfaces gives a precise
universal prescription for the monotonous quantity in the c-theorem for d=3.
This is in principle computable using any regularization for the entropy, and
in particular is a definition suitable for lattice models. We rederive the
proof of the c-theorem for d=3 in terms of mutual information, and check our
arguments with holographic entanglement entropy, a free scalar field, and an
extensive mutual information model.Comment: 80 pages, 16 figure
Holographic c-theorems in arbitrary dimensions
We re-examine holographic versions of the c-theorem and entanglement entropy
in the context of higher curvature gravity and the AdS/CFT correspondence. We
select the gravity theories by tuning the gravitational couplings to eliminate
non-unitary operators in the boundary theory and demonstrate that all of these
theories obey a holographic c-theorem. In cases where the dual CFT is
even-dimensional, we show that the quantity that flows is the central charge
associated with the A-type trace anomaly. Here, unlike in conventional
holographic constructions with Einstein gravity, we are able to distinguish
this quantity from other central charges or the leading coefficient in the
entropy density of a thermal bath. In general, we are also able to identify
this quantity with the coefficient of a universal contribution to the
entanglement entropy in a particular construction. Our results suggest that
these coefficients appearing in entanglement entropy play the role of central
charges in odd-dimensional CFT's. We conjecture a new c-theorem on the space of
odd-dimensional field theories, which extends Cardy's proposal for even
dimensions. Beyond holography, we were able to show that for any
even-dimensional CFT, the universal coefficient appearing the entanglement
entropy which we calculate is precisely the A-type central charge.Comment: 62 pages, 4 figures, few typo's correcte
Thermodynamical property of entanglement entropy and deconfinement phase transition
We analyze the holographic entanglement entropy in a soliton background with
Wilson lines and derive a relation analogous to the first law of
thermodynamics. The confinement/deconfinement phase transition occurs due to
the competition of two minimal surfaces. The entropic c function probes the
confinement/deconfinement phase transition. It is sensitive to the degrees of
freedom (DOF) smaller than the size of a spatial circle. When the Wilson line
becomes large, the entropic c function becomes non-monotonic as a function of
the size and does not satisfy the usual c-theorem. We analyze the entanglement
entropy for a small subregion and the relation analogous to the first law of
thermodynamics. For the small amount of Wilson lines, the excited amount of the
entanglement entropy decreases from the ground state. It reflects that
confinement decreases degrees of freedom. We finally discuss the second order
correction of the holographic entanglement entropy.Comment: 25 pages, 5 figures; v2 minor changes, references adde
A finite entanglement entropy and the c-theorem
The trace over the degrees of freedom located in a subset of the space
transforms the vacuum state into a mixed density matrix with non zero entropy.
This is usually called entanglement entropy, and it is known to be divergent in
quantum field theory (QFT). However, it is possible to define a finite quantity
F(A,B) for two given different subsets A and B which measures the degree of
entanglement between their respective degrees of freedom. We show that the
function F(A,B) is severely constrained by the Poincare symmetry and the
mathematical properties of the entropy. In particular, for one component sets
in two dimensional conformal field theories its general form is completely
determined. Moreover, it allows to prove an alternative entropic version of the
c-theorem for 1+1 dimensional QFT. We propose this well defined quantity as the
meaningfull entanglement entropy and comment on possible applications in QFT
and the black hole evaporation problem.Comment: 11 pages, 3 figures, added references and erratu
Refined Holographic Entanglement Entropy for the AdS Solitons and AdS black Holes
We consider the refinement of the holographic entanglement entropy for the
holographic dual theories to the AdS solitons and AdS black holes, including
the corrected ones by the Gauss-Bonnet term. The refinement is obtained by
extracting the UV-independent piece of the holographic entanglement entropy,
the so-called renormalized entanglement entropy which is independent of the
choices of UV cutoff. Our main results are (i) the renormalized entanglement
entropies of the AdS soliton for are neither monotonically
decreasing along the RG flow nor positive definite, especially around the
deconfinement/confinement phase transition; (ii) there is no topological
entanglement entropy for AdS soliton even with Gauss-Bonnet correction;
(iii) for the AdS black holes, the renormalized entanglement entropy obeys an
expected volume law at IR regime, and the transition between UV and IR regimes
is a smooth crossover even with Gauss-Bonnet correction; (iv) based on AdS/MERA
conjecture, we postulate that the IR fixed-point state for the non-extremal AdS
soliton is a trivial product state.Comment: 48 pages, 24 figures; v2: few typos corrected; v3: mistake on the
choice of dominant phase is corrected, differential subtraction scheme is
introduced to remove the UV cutoff-ambiguity, some of the conclusions on RG
flow are changed; v4: statement about C theorem revised; v5 Final version to
NP
- …