78 research outputs found
Aspects of AdS/BCFT
We expand the results of arXiv:1105.5165, where a holographic description of
a conformal field theory defined on a manifold with boundaries (so called BCFT)
was proposed, based on AdS/CFT. We construct gravity duals of conformal field
theories on strips, balls and also time-dependent boundaries. We show a
holographic g-theorem in any dimension. As a special example, we can define a
`boundary central charge' in three dimensional conformal field theories and our
holographic g-theorem argues that it decreases under RG flows. We also computed
holographic one-point functions and confirmed that their scaling property
agrees with field theory calculations. Finally, we give an example of string
theory embedding of this holography by inserting orientifold 8-planes in
AdS(4)xCP(3).Comment: 41 pages, 10 figures; v2: further comments on earlier papers about a
holographic dual with boundarie
Holographic entanglement entropy: near horizon geometry and disconnected regions
We study the finite term of the holographic entanglement entropy for the charged black hole in AdS(d+2) and other examples of black holes when the spatial region in the boundary theory is given by one or two parallel strips. For one large strip it scales like the width of the strip. The divergent term of its expansion as the turning point of the minimal surface approaches the horizon is determined by the near horizon geometry. Examples involving a Lifshitz scaling are also considered. For two equal strips in the boundary we study the transition of the mutual information given by the holographic prescription. In the case of the charged black hole, when the width of the strips becomes large this transition provides a characteristic finite distance depending on the temperature
Modular conjugations in 2D conformal field theory and holographic bit threads
We study the geometric action of some modular conjugations in two dimensional
(2D) conformal field theories. We investigate the bipartition given by an
interval when the system is in the ground state, either on the line or on the
circle, and in the thermal Gibbs state on the line. We find that the
restriction of the corresponding inversion maps to a spatial slice is obtained
also in the gauge/gravity correspondence through the geodesic bit threads in a
constant time slice of the dual static asymptotically AdS background. For a CFT
in the thermal state on the line, the modular conjugation suggests the
occurrence of a second world which can be related through the geodesic bit
threads to the horizon of the BTZ black brane background. An inversion map is
constructed also for the massless Dirac fermion in the ground state and on the
line bipartite by the union of two disjoint intervals.Comment: 49 pages, 15 figure
Giant magnons and spiky strings on the conifold
We find explicit solutions for giant magnons and spiky strings on the squashed three dimensional sphere. For a special value of the squashing parameter the solutions describe strings moving in a sector of the conifold, while for another value of the squashing parameter we recover the known results on the round three dimensional sphere. A new feature is that the energy and the momenta enter in the dispersion relation of the conifold in a transcendental way
On the continuum limit of the entanglement Hamiltonian of a sphere for the free massless scalar field
We study the continuum limit of the entanglement Hamiltonian of a sphere for the massless scalar field in its ground state by employing the lattice model defined through the discretisation of the radial direction. In two and three spatial dimensions and for small values of the total angular momentum, we find numerical results in agreement with the corresponding ones derived from the entanglement Hamiltonian predicted by conformal field theory. When the mass parameter in the lattice model is large enough, the dominant contributions come from the on-site and the nearest-neighbour terms, whose weight functions are straight lines
On entanglement Hamiltonians of an interval in massless harmonic chains
We study the continuum limit of the entanglement Hamiltonians of a block of consecutive sites in massless harmonic chains. This block is either in the chain on the infinite line or at the beginning of a chain on the semi-infinite line with Dirichlet boundary conditions imposed at its origin. The entanglement Hamiltonians of the interval predicted by conformal field theory (CFT) for the massless scalar field are obtained in the continuum limit. We also study the corresponding entanglement spectra, and the numerical results for the ratios of the gaps are compatible with the operator content of the boundary CFT of a massless scalar field with Neumann boundary conditions imposed along the boundaries introduced around the entangling points by the regularisation procedure
Entanglement entropy of two disjoint intervals in conformal field theory: II
We continue the study of the entanglement entropy of two disjoint intervals in conformal field theories that we started in Calabrese et al 2009 J. Stat. Mech. P11001. We compute Tr rho(n)(A) for any integer n for the Ising universality class and the final result is expressed as a sum of Riemann-Siegel theta functions. These predictions are checked against existing numerical data. We provide a systematic method that gives the full asymptotic expansion of the scaling function for small four-point ratio (i.e. short intervals). These formulas are compared with the direct expansion of the full results for a free compactified boson and Ising model. We finally provide the analytic continuation of the first term in this expansion in a completely analytic form
Entanglement negativity in quantum field theory
We develop a systematic method to extract the negativity in the ground state
of a 1+1 dimensional relativistic quantum field theory, using a path integral
formalism to construct the partial transpose rho_A^{T_2} of the reduced density
matrix of a subsystem A=A1 U A2, and introducing a replica approach to obtain
its trace norm which gives the logarithmic negativity E=ln||\rho_A^{T_2}||.
This is shown to reproduce standard results for a pure state. We then apply
this method to conformal field theories, deriving the result E\sim(c/4) ln(L1
L2/(L1+L2)) for the case of two adjacent intervals of lengths L1, L2 in an
infinite system, where c is the central charge. For two disjoint intervals it
depends only on the harmonic ratio of the four end points and so is manifestly
scale invariant. We check our findings against exact numerical results in the
harmonic chain.Comment: 4 pages, 5 figure
Local and non-local properties of the entanglement Hamiltonian for two disjoint intervals
We consider free-fermion chains in the ground state and the entanglement Hamiltonian for a subsystem consisting of two separated intervals. In this case, one has a peculiar long-range hopping between the intervals in addition to the well-known and dominant short-range hopping. We show how the continuum expressions can be recovered from the lattice results for general filling and arbitrary intervals. We also discuss the closely related case of a single interval located at a certain distance from the end of a semi-infinite chain and the continuum limit for this problem. Finally, we show that for the double interval in the continuum a commuting operator exists which can be used to find the eigenstates
Entanglement entropies of an interval in the free Schrödinger field theory on the half line
We study the entanglement entropies of an interval adjacent to the boundary of the half line for the free fermionic spinless Schrodinger field theory at finite density and zero temperature, with either Neumann or Dirichlet boundary conditions. They are finite functions of the dimensionless parameter given by the product of the Fermi momentum and the length of the interval. The entanglement entropy displays an oscillatory behaviour, differently from the case of the interval on the whole line. This behaviour is related to the Friedel oscillations of the mean particle density on the half line at the entangling point. We find analytic expressions for the expansions of the entanglement entropies in the regimes of small and large values of the dimensionless parameter. They display a remarkable agreement with the curves obtained numerically. The analysis is extended to a family of free fermionic Lifshitz models labelled by their integer Lifshitz exponent, whose parity determines the properties of the entanglement entropies. The cumulants of the local charge operator and the Schatten norms of the underlying kernels are also explored
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