190 research outputs found
Conformal Bootstrap in the Regge Limit
We analytically solve the conformal bootstrap equations in the Regge limit
for large N conformal field theories. For theories with a parametrically large
gap, the amplitude is dominated by spin-2 exchanges and we show how the
crossing equations naturally lead to the construction of AdS exchange Witten
diagrams. We also show how this is encoded in the anomalous dimensions of
double-trace operators of large spin and large twist. We use the chaos bound to
prove that the anomalous dimensions are negative. Extending these results to
correlators containing two scalars and two conserved currents, we show how to
reproduce the CEMZ constraint that the three-point function between two
currents and one stress tensor only contains the structure given by
Einstein-Maxwell theory in AdS, up to small corrections. Finally, we consider
the case where operators of unbounded spin contribute to the Regge amplitude,
whose net effect is captured by summing the leading Regge trajectory. We
compute the resulting anomalous dimensions and corrections to OPE coefficients
in the crossed channel and use the chaos bound to show that both are negative.Comment: 40 pages, 1 figure; V2: Small corrections and clarification
Bulk Matter and the Boundary Quantum Null Energy Condition
We investigate the quantum null energy condition (QNEC) in holographic CFTs,
focusing on half-spaces and particular classes of states. We present direct,
and in certain cases nonperturbative, calculations for both the diagonal and
off- diagonal variational derivatives of entanglement entropy. In d > 2, we
find that the QNEC is saturated. We compute relations between the off-diagonal
variation of entanglement, boundary relative entropy, and the bulk stress
tensor. Strong subadditivity then leads to energy conditions in the bulk. In d
= 2, we find that the QNEC is in general not saturated when the Ryu-Takayanagi
surface intersects bulk matter. Moreover, when bulk matter is present the QNEC
can imply new bulk energy conditions. For a simple class of states, we derive
an example that is stronger than the bulk averaged null energy condition and
reduces to it in certain limits.Comment: 22 page
A Numerical Approach to Virasoro Blocks and the Information Paradox
We chart the breakdown of semiclassical gravity by analyzing the Virasoro
conformal blocks to high numerical precision, focusing on the heavy-light limit
corresponding to a light probe propagating in a BTZ black hole background. In
the Lorentzian regime, we find empirically that the initial exponential
time-dependence of the blocks transitions to a universal
power-law decay. For the vacuum block the transition occurs at , confirming analytic predictions. In the Euclidean regime,
due to Stokes phenomena the naive semiclassical approximation fails completely
in a finite region enclosing the `forbidden singularities'. We emphasize that
limitations on the reconstruction of a local bulk should ultimately stem from
distinctions between semiclassical and exact correlators.Comment: 45 pages, 23 figure
Exact Virasoro Blocks from Wilson Lines and Background-Independent Operators
Aspects of black hole thermodynamics and information loss can be derived as a
consequence of Virasoro symmetry. To bolster the connection between Virasoro
conformal blocks and AdS quantum gravity, we study sl Chern-Simons
Wilson line networks and revisit the idea that they compute a variety of
CFT observables, including Virasoro OPE blocks, exactly. We verify this in
the semiclassical large central charge limit and to low orders in a
perturbative expansion.
Wilson lines connecting the boundary to points in the bulk play a natural
role in bulk reconstruction. Because quantum gravity in AdS is rigidly
fixed by Virasoro symmetry, we argue that sl Wilson lines provide building
blocks for background independent bulk reconstruction. In particular, we show
explicitly that they automatically compute the uniformizing coordinates
appropriate to any background state.Comment: V3- Added some references V2- Significantly Expanded Appendix on
Regulation; 32+21 page
The Bulk-to-Boundary Propagator in Black Hole Microstate Backgrounds
First-quantized propagation in quantum gravitational AdS backgrounds can
be exactly reconstructed using CFT data and Virasoro symmetry. We develop
methods to compute the bulk-to-boundary propagator in a black hole microstate,
, at finite
central charge. As a first application, we show that the semiclassical theory
on the Euclidean BTZ solution sharply disagrees with the exact description, as
expected based on the resolution of forbidden thermal singularities, though
this effect may appear exponentially small for physical observers.Comment: 34+27 pages, 7 figures; v2: typos correcte
The AdS Propagator and the Fate of Locality
We recently used Virasoro symmetry considerations to propose an exact formula
for a bulk proto-field in AdS. In this paper we study the propagator
. We show that many techniques from the study of
conformal blocks can be generalized to compute it, including the semiclassical
monodromy method and both forms of the Zamolodchikov recursion relations. When
the results from recursion are expanded at large central charge, they match
gravitational perturbation theory for a free scalar field coupled to gravity in
our chosen gauge.
We find that although the propagator is finite and well-defined at long
distances, its perturbative expansion in exhibits UV/IR
mixing effects. If we nevertheless interpret as a
probe of bulk locality, then when locality breaks down at
the new short-distance scale . For
with very large bulk mass, or at small central charge, bulk locality
fails at the AdS length scale. In all cases, locality `breakdown' manifests as
singularities or branch cuts at spacelike separation arising from
non-perturbative quantum gravitational effects.Comment: 42+17 pages, 7 figure
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