186 research outputs found
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
Constraints on Flavored 2d CFT Partition Functions
We study the implications of modular invariance on 2d CFT partition functions
with abelian or non-abelian currents when chemical potentials for the charges
are turned on, i.e. when the partition functions are "flavored". We begin with
a new proof of the transformation law for the modular transformation of such
partition functions. Then we proceed to apply modular bootstrap techniques to
constrain the spectrum of charged states in the theory. We improve previous
upper bounds on the state with the greatest "mass-to-charge" ratio in such
theories, as well as upper bounds on the weight of the lightest charged state
and the charge of the weakest charged state in the theory. We apply the
extremal functional method to theories that saturate such bounds, and in
several cases we find the resulting prediction for the occupation numbers are
precisely integers. Because such theories sometimes do not saturate a bound on
the full space of states but do saturate a bound in the neutral sector of
states, we find that adding flavor allows the extremal functional method to
solve for some partition functions that would not be accessible to it
otherwise.Comment: 45 pages, 16 Figures v3: typos corrected, expanded appendix on
numeric implementatio
(Extra)Ordinary Gauge Mediation
We study models of "(extra)ordinary gauge mediation," which consist of taking
ordinary gauge mediation and extending the messenger superpotential to include
all renormalizable couplings consistent with SM gauge invariance and an
R-symmetry. We classify all such models and find that their phenomenology can
differ significantly from that of ordinary gauge mediation. Some highlights
include: arbitrary modifications of the squark/slepton mass relations, small mu
and Higgsino NLSP's, and the possibility of having fewer than one effective
messenger. We also show how these models lead naturally to extremely simple
examples of direct gauge mediation, where SUSY and R-symmetry breaking occur
not in a hidden sector, but due to the dynamics of the messenger sector itself.Comment: 50 pages, 11 figure
- β¦