603 research outputs found
Permutation Orbifolds and Chaos
We study out-of-time-ordered correlation functions in permutation orbifolds
at large central charge. We show that they do not decay at late times for
arbitrary choices of low-dimension operators, indicating that permutation
orbifolds are non-chaotic theories. This is in agreement with the fact they are
free discrete gauge theories and should be integrable rather than chaotic. We
comment on the early-time behaviour of the correlators as well as the
deformation to strong coupling.Comment: 15 pages, v2: more references and additional comments in the
introductio
Einstein gravity from ANEC correlators
We study correlation functions with multiple averaged null energy (ANEC)
operators in conformal field theories. For large CFTs with a large gap to
higher spin operators, we show that the OPE between a local operator and the
ANEC can be recast as a particularly simple differential operator acting on the
local operator. This operator is simple enough that we can resum it and obtain
the finite distance OPE. Under the large - large gap assumptions, the
vanishing of the commutator of ANEC operators tightly constrains the OPE
coefficients of the theory. An important example of this phenomenon is the
conclusion that in . This implies that the bulk dual of such a CFT
is semi-classical Einstein-gravity with minimally coupled matter.Comment: 32 pages + appendices, 6 figures; v2:typos corrected and a comment
added in introductio
Comments on a state-operator correspondence for the torus
We investigate the existence of a state-operator correspondence on the torus.
This correspondence would relate states of the CFT Hilbert space living on a
spatial torus to the path integral over compact Euclidean manifolds with
operator insertions. Unlike the states on the sphere that are associated to
local operators, we argue that those on the torus would more naturally be
associated to line operators. We find evidence that such a correspondence
cannot exist and in particular, we argue that no compact Euclidean path
integral can produce the vacuum on the torus. Our arguments come solely from
field theory and formulate a CFT version of the Horowitz-Myers conjecture for
the AdS soliton.Comment: 29 pages, 8 figure
Genus Two Partition Functions and Renyi Entropies of Large c CFTs
We compute genus two partition functions in two dimensional conformal field
theories at large central charge, focusing on surfaces that give the third
Renyi entropy of two intervals. We compute this for generalized free theories
and for symmetric orbifolds, and compare it to the result in pure gravity. We
find a new phase transition if the theory contains a light operator of
dimension . This means in particular that unlike the second
Renyi entropy, the third one is no longer universal.Comment: 28 pages + Appendice
Sub-AdS Scale Locality in AdS/CFT
We investigate sub-AdS scale locality in a weakly coupled toy model of the
AdS/CFT correspondence. We find that this simple model has the correct
density of states at low and high energies to be dual to Einstein gravity
coupled to matter in AdS. Bulk correlation functions also have the correct
behavior at leading order in the large expansion, but non-local effects
emerge at order . Our analysis leads to the conjecture that any large
CFT that is modular invariant and has the right low-energy density of
states is dual to a gravitational theory with sub-AdS scale locality.Comment: 19 page
From sources to initial data and back again: on bulk singularities in Euclidean AdS/CFT
A common method to prepare states in AdS/CFT is to perform the Euclidean path
integral with sources turned on for single-trace operators. These states can be
interpreted as coherent states of the bulk quantum theory associated to
Lorentzian initial data on a Cauchy slice. In this paper, we discuss the extent
to which arbitrary initial data can be obtained in this way. We show that the
initial data must be analytic and define the subset of it that can be prepared
by imposing bulk regularity. Turning this around, we show that for generic
analytic initial data the corresponding Euclidean section contains
singularities coming from delta function sources in the bulk. We propose an
interpretation of these singularities as non-perturbative objects in the
microscopic theory.Comment: 16 pages, 6 figure
Random Statistics of OPE Coefficients and Euclidean Wormholes
We propose an ansatz for OPE coefficients in chaotic conformal field theories
which generalizes the Eigenstate Thermalization Hypothesis and describes any
OPE coefficient involving heavy operators as a random variable with a Gaussian
distribution. In two dimensions this ansatz enables us to compute higher
moments of the OPE coefficients and analyse two and four-point functions of OPE
coefficients, which we relate to genus-2 partition functions and their squares.
We compare the results of our ansatz to solutions of Einstein gravity in
AdS, including a Euclidean wormhole that connects two genus-2 surfaces. Our
ansatz reproduces the non-perturbative correction of the wormhole, giving it a
physical interpretation in terms of OPE statistics. We propose that
calculations performed within the semi-classical low-energy gravitational
theory are only sensitive to the random nature of OPE coefficients, which
explains the apparent lack of factorization in products of partition functions.Comment: 7 pages, 3 figures; v2, minor comments and references added, version
as appearing in CQ
Complexity and the bulk volume, a new York time story
We study the boundary description of the volume of maximal Cauchy slices
using the recently derived equivalence between bulk and boundary symplectic
forms. The volume of constant mean curvature slices is known to be canonically
conjugate to "York time". We use this to construct the boundary deformation
that is conjugate to the volume in a handful of examples, such as empty AdS, a
backreacting scalar condensate, or the thermofield double at infinite time. We
propose a possible natural boundary interpretation for this deformation and use
it to motivate a concrete version of the complexity=volume conjecture, where
the boundary complexity is defined as the energy of geodesics in the K\"ahler
geometry of half sided sources. We check this conjecture for Ba\~nados
geometries and a mini-superspace version of the thermofield double state.
Finally, we show that the precise dual of the quantum information metric for
marginal scalars is given by a particularly simple symplectic flux, instead of
the volume as previously conjectured.Comment: 43 pages + appendices, 5 figures; v2: typos fixed, small comments
added
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