3,162 research outputs found
One loop partition function in AdS_3/CFT_2
The 1-loop partition function of the handle-body solutions in the AdS
gravity have been derived some years ago using the heat-kernel and the method
of images. In the semiclassical limit, such partition function should
correspond to the order part in the partition function of dual
conformal field theory on the boundary Riemann surface. The higher genus
partition function could be computed by the multi-point functions in the
Riemann sphere via sewing prescription. In the large central charge limit, to
the leading order of , the multi-point function is further simplified to be
a summation over the product of two-point functions, which may form links. Each
link is in one-to-one correspondence with the conjugacy class of the Schottky
group of the Riemann surface. Moreover, the value of a link is determined by
the eigenvalue of the element in the conjugate class. This allows us to
reproduce exactly the gravitational 1-loop partition function. The proof can be
generalized to the higher spin gravity and its dual CFT.Comment: 30 pages, 8 figures; typos corrected, more clarifications, references
and acknowledgements adde
R\'enyi Entropy of Free Compact Boson on Torus
In this paper, we reconsider the single interval R\'enyi entropy of a free
compact scalar on a torus. In this case, the contribution to the entropy could
be decomposed into classical part and quantum part. The classical part includes
the contribution from all the saddle points, while the quantum part is
universal. After considering a different monodromy condition from the one in
the literature, we re-evaluate the classical part of the R\'enyi entropy.
Moreover, we expand the entropy in the low temperature limit and find the
leading thermal correction term which is consistent with the universal behavior
suggested in arXiv:1403.0578 [hep-th]. Furthermore we investigate the large
interval behavior of the entanglement entropy and show that the universal
relation between the entanglement entropy and thermal entropy holds in this
case.Comment: 16 pages. Improved arguments, added referenc
Quantum dynamics in sine-square deformed conformal field theory: Quench from uniform to non-uniform CFTs
In this work, motivated by the sine-square deformation (SSD) for
(1+1)-dimensional quantum critical systems, we study the non-equilibrium
quantum dynamics of a conformal field theory (CFT) with SSD, which was recently
proposed to have continuous energy spectrum and continuous Virasoro algebra. In
particular, we study the time evolution of entanglement entropy after a quantum
quench from a uniform CFT, which is defined on a finite space of length , to
a sine-square deformed CFT. We find there is a crossover time that
divides the entanglement evolution into two interesting regions. For , the entanglement entropy does not evolve in time; for , the entanglement entropy grows as ,
which is independent of the lengths of the subsystem and the total system. This
growth with no revival indicates that a sine-square deformed CFT
effectively has an infinite length, in agreement with previous studies based on
the energy spectrum analysis. Furthermore, we study the quench dynamics for a
CFT with Mbius deformation, which interpolates between a
uniform CFT and a sine-square deformed CFT. The entanglement entropy oscillates
in time with period , with
corresponding to the uniform case and corresponding to the
SSD limit. Our field theory calculation is confirmed by a numerical study on a
(1+1)-d critical fermion chain.Comment: are welcome; 10 pages, 4 figures; v2: refs added; v3: refs added; A
physical interpretation of t* is added; v4: published version (selected as
Editors' Suggestion
Holographic Calculation for Large Interval R\'enyi Entropy at High Temperature
In this paper, we study the holographic R\'enyi entropy of a large interval
on a circle at high temperature for the two-dimensional conformal field theory
(CFT) dual to pure AdS gravity. In the field theory, the R\'enyi entropy is
encoded in the CFT partition function on -sheeted torus connected with each
other by a large branch cut. As proposed by Chen and Wu [Large interval limit
of R\'enyi entropy at high temperature, arXiv:1412.0763], the effective way to
read the entropy in the large interval limit is to insert a complete set of
state bases of the twist sector at the branch cut. Then the calculation
transforms into an expansion of four-point functions in the twist sector with
respect to . By using the operator product expansion of
the twist operators at the branch points, we read the first few terms of the
R\'enyi entropy, including the leading and next-to-leading contributions in the
large central charge limit. Moreover, we show that the leading contribution is
actually captured by the twist vacuum module. In this case by the Ward identity
the four-point functions can be derived from the correlation function of four
twist operators, which is related to double interval entanglement entropy.
Holographically, we apply the recipe in [T. Faulkner, The entanglement R\'enyi
entropies of disjoint intervals in AdS/CFT, arXiv:1303.7221] and [T. Barrella
et al., Holographic entanglement beyond classical gravity, J. High Energy Phys.
09 (2013) 109] to compute the classical R\'enyi entropy and its one-loop
quantum correction, after imposing a new set of monodromy conditions. The
holographic classical result matches exactly with the leading contribution in
the field theory up to and , while the holographical
one-loop contribution is in exact agreement with next-to-leading results in
field theory up to and as well.Comment: minor corrections, match with the published versio
Entanglement, Replicas, and Thetas
We compute the single-interval Renyi entropy (replica partition function) for
free fermions in 1+1d at finite temperature and finite spatial size by two
methods: (i) using the higher-genus partition function on the replica Riemann
surface, and (ii) using twist operators on the torus. We compare the two
answers for a restricted set of spin structures, leading to a non-trivial
proposed equivalence between higher-genus Siegel -functions and Jacobi
-functions. We exhibit this proposal and provide substantial evidence
for it. The resulting expressions can be elegantly written in terms of Jacobi
forms. Thereafter we argue that the correct Renyi entropy for modular-invariant
free-fermion theories, such as the Ising model and the Dirac CFT, is given by
the higher-genus computation summed over all spin structures. The result
satisfies the physical checks of modular covariance, the thermal entropy
relation, and Bose-Fermi equivalence.Comment: 34 page
Entanglement Entropy for Descendent Local Operators in 2D CFTs
We mainly study the R\'enyi entropy and entanglement entropy of the states
locally excited by the descendent operators in two dimensional conformal field
theories (CFTs). In rational CFTs, we prove that the increase of entanglement
entropy and R\'enyi entropy for a class of descendent operators, which are
generated by onto the primary operator,
always coincide with the logarithmic of quantum dimension of the corresponding
primary operator. That means the R\'enyi entropy and entanglement entropy for
these descendent operators are the same as the ones of their corresponding
primary operator. For 2D rational CFTs with a boundary, we confirm that the
R\'enyi entropy always coincides with the logarithmic of quantum dimension of
the primary operator during some periods of the evolution. Furthermore, we
consider more general descendent operators generated by on the primary
operator. For these operators, the entanglement entropy and R\'enyi entropy get
additional corrections, as the mixing of holomorphic and anti-holomorphic
Virasoro generators enhance the entanglement. Finally, we employ perturbative
CFT techniques to evaluate the R\'enyi entropy of the excited operators in
deformed CFT. The R\'enyi and entanglement entropies are increased, and get
contributions not only from local excited operators but also from global
deformation of the theory.Comment: 30 pages, 2 figures; minor revion, references adde
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