1,462 research outputs found
An Effective Theory for Holographic RG Flows
We study the dilaton action induced by RG flows between holographic CFT fixed
points. For this purpose we introduce a general bulk effective theory for the
goldstone boson of the broken spacetime symmetry, providing an AdS analog of
the EFT of Inflation. In two dimensions, we use the effective theory to compute
the dilaton action, as well as the UV and IR conformal anomalies, without
further assumptions. In higher dimensions we take a `slow-flow' limit analogous
to the assumption of slow-roll in Inflation, and in this context we obtain the
dilaton action, focusing on terms proportional to the difference of the A-type
anomalies. We include Gauss-Bonnet terms in the gravitational action in order
to verify that our method correctly differentiates between A-type and other
anomalies.Comment: 36 Pages (23 pages main text; 13 Pages Appendix); 3 figure
Conformal Blocks Beyond the Semi-Classical Limit
Black hole microstates and their approximate thermodynamic properties can be
studied using heavy-light correlation functions in AdS/CFT. Universal features
of these correlators can be extracted from the Virasoro conformal blocks in
CFT2, which encapsulate quantum gravitational effects in AdS3. At infinite
central charge c, the Virasoro vacuum block provides an avatar of the black
hole information paradox in the form of periodic Euclidean-time singularities
that must be resolved at finite c.
We compute Virasoro blocks in the heavy-light, large c limit, extending our
previous results by determining perturbative 1/c corrections. We obtain
explicit closed-form expressions for both the `semi-classical'
and `quantum' corrections to the vacuum block, and we provide
integral formulas for general Virasoro blocks. We comment on the interpretation
of our results for thermodynamics, discussing how monodromies in Euclidean time
can arise from AdS calculations using `geodesic Witten diagrams'. We expect
that only non-perturbative corrections in 1/c can resolve the singularities
associated with the information paradox.Comment: 24+7 pages, 5 figures; v2 fixed typo in eq 2.22, added refs; v3 fixed
typo
A Quantum Correction To Chaos
We use results on Virasoro conformal blocks to study chaotic dynamics in
CFT at large central charge c. The Lyapunov exponent , which is
a diagnostic for the early onset of chaos, receives corrections that may
be interpreted as . However, out of time order correlators receive other equally
important suppressed contributions that do not have such a simple
interpretation. We revisit the proof of a bound on that emerges at
large , focusing on CFT and explaining why our results do not conflict
with the analysis leading to the bound. We also comment on relationships
between chaos, scattering, causality, and bulk locality.Comment: 22+6 pages, 6 figure
On the Late-Time Behavior of Virasoro Blocks and a Classification of Semiclassical Saddles
Recent work has demonstrated that black hole thermodynamics and information
loss/restoration in AdS/CFT can be derived almost entirely from the
behavior of the Virasoro conformal blocks at large central charge, with
relatively little dependence on the precise details of the CFT spectrum or OPE
coefficients. Here, we elaborate on the non-perturbative behavior of Virasoro
blocks by classifying all `saddles' that can contribute for arbitrary values of
external and internal operator dimensions in the semiclassical large central
charge limit. The leading saddles, which determine the naive semiclassical
behavior of the Virasoro blocks, all decay exponentially at late times, and at
a rate that is independent of internal operator dimensions. Consequently, the
semiclassical contribution of high-energy states does not resolve a well-known
version of the information loss problem in AdS. However, we identify two
infinite classes of sub-leading saddles, and one of these classes does not
decay at late times.Comment: 38+10 pages, 17 figures; v2: added refs, comment
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