217 research outputs found
Universal corrections to entanglement entropy of local quantum quenches
We study the time evolution of single interval Renyi and entanglement entropies following local quantum quenches in two dimensional conformal field theories at finite temperature for which the locally excited states have a finite temporal width, \epsilon. We show that, for local quenches produced by the action of a conformal primary field, the time dependence of Renyi and entanglement entropies at order \epsilon^2 is universal. It is determined by the expectation value of the stress tensor in the replica geometry and proportional to the conformal dimension of the primary field generating the local excitation. We also show that in CFTs with a gravity dual, the \epsilon^2 correction to the holographic entanglement entropy following a local quench precisely agrees with the CFT prediction. We then consider CFTs admitting a higher spin symmetry and turn on a higher spin chemical potential \mu. We calculate the time dependence of the order \epsilon^2 correction to the entanglement entropy for small \mu, and show that the contribution at order \mu^2 is universal. We verify our arguments against exact results for minimal models and the free fermion theory
Scrambling time from local perturbations of the eternal BTZ black hole
We compute the mutual information between finite intervals in two non-compact
2d CFTs in the thermofield double formulation after one of them has been
locally perturbed by a primary operator at some time in the large
limit. We determine the time scale, called the scrambling time, at which
the mutual information vanishes and the original entanglement between the
thermofield double gets destroyed by the perturbation. We provide a holographic
description in terms of a free falling particle in the eternal BTZ black hole
that exactly matches our CFT calculations. Our results hold for any time
. In particular, when the latter is large, they reproduce the bulk
shock-wave propagation along the BTZ horizon description.Comment: 37 pages, 5 figure
Summing Up All Genus Free Energy of ABJM Matrix Model
The localization technique allows us to compute the free energy of the U(N)_k
x U(N)_{-k} Chern-Simons-matter theory dual to type IIA strings on AdS_4 x CP^3
from weak to strong 't Hooft coupling \lambda = N / k at finite N, as
demonstrated by Drukker, Marino, and Putrov. In this note we study further the
free energy at large 't Hooft coupling with the aim of testing AdS/CFT at the
quantum gravity level and, in particular, sum up all the 1/N corrections, apart
from the worldsheet instanton contributions. The all genus partition function
takes a remarkably simple form -- the Airy function, Ai (k^{4/3} \lambda_r),
with the renormalized 't Hooft coupling \lambda_r.Comment: 18 pages, no figures, v2: typos corrected and references adde
Local quenches and quantum chaos from higher spin perturbations
We study local quenches in 1+1 dimensional conformal field theories at large-c by operators carrying higher spin charge. Viewing such states as solutions in Chern-Simons theory, representing infalling massive particles with spin-three charge in the BTZ back- ground, we use the Wilson line prescription to compute the single-interval entanglement entropy (EE) and scrambling time following the quench. We find that the change in EE is finite (and real) only if the spin-three charge q is bounded by the energy of the perturbation E, as |q|/c < E^2/c^2. We show that the Wilson line/EE correlator deep in the quenched regime and its expansion for small quench widths overlaps with the Regge limit for chaos of the out-of-time-ordered correlator. We further find that the scrambling time for the two- sided mutual information between two intervals in the thermofield double state increases with increasing spin-three charge, diverging when the bound is saturated. For larger values of the charge, the scrambling time is shorter than for pure gravity and controlled by the spin-three Lyapunov exponent 4π/β. In a CFT with higher spin chemical potential, dual to a higher spin black hole, we find that the chemical potential must be bounded to ensure that the mutual information is a concave function of time and entanglement speed is less than the speed of light. In this case, a quench with zero higher spin charge yields the same Lyapunov exponent as pure Einstein gravity
Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3
We review the duality and integrability of N=6 superconformal Chern-Simons
theory in three dimensions and IIA superstring theory on the background
AdS4xCP3. We introduce both of these models and describe how their degrees of
freedom are mapped to excitations of a long-range integrable spin-chain.
Finally, we discuss the properties of the Bethe equations, the S-matrix and the
algebraic curve that are special to this correspondence and differ from the
case of N=4 SYM theory and strings on AdS5xS5.Comment: 22 pages, see also overview article arXiv:1012.3982, v2: references
to other chapters updated, v3: references added, v4: brief discussion of
giant magnons added, further minor changes, published version, v5: union of
v3 and v4 because changes made in v3 were accidentally lost in v
Form factors of chiral primary operators at two loops in ABJ(M)
archiveprefix: arXiv primaryclass: hep-th reportnumber: NORDITA-2013-34 slaccitation: %%CITATION = ARXIV:1305.2422;%%archiveprefix: arXiv primaryclass: hep-th reportnumber: NORDITA-2013-34 slaccitation: %%CITATION = ARXIV:1305.2422;%%archiveprefix: arXiv primaryclass: hep-th reportnumber: NORDITA-2013-34 slaccitation: %%CITATION = ARXIV:1305.2422;%
Quivers, words and fundamentals
40 pages + Appendices, 9 figures40 pages + Appendices, 9 figure
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