General results for higher spin Wilson lines and entanglement in Vasiliev theory

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.Comment: References added, 56 pages, 9 figure

Section: Discussionmentioning

confidence: 99%

Universal corrections to entanglement entropy of local quantum quenches

David

Khetrapal

Kumar

2016

“…We then have 20) where the z dependence is immediately fixed by rotational symmetry on the disk. To close this section, we should also mention that the most intuitive explanation for the form of the Wilson line comes from thinking about the AdS 3 /CFT 2 correspondence, and in particular from the fact that AdS 3 gravity is equivalent to SL(2)×SL(2) Chern-Simons theory; actually, these constructions originated in higher spin extensions [25][26][27][28]. Asymptotically AdS 3 solutions of Einstein's equations (which are all locally AdS 3 since there are no dynamical degrees of freedom) are recast as flat connections.…”

Section: )mentioning

confidence: 99%

Late time Wilson lines

Kraus¹,

Sivaramakrishnan²,

Snively³

2019

Self Cite

In the AdS 3 /CFT 2 correspondence, physical interest attaches to understanding Virasoro conformal blocks at large central charge and in a kinematical regime of large Lorentzian time separation, t ∼ c. However, almost no analytical information about this regime is presently available. By employing the Wilson line representation we derive new results on conformal blocks at late times, effectively resumming all dependence on t/c. This is achieved in the context of "light-light" blocks, as opposed to the richer, but much less tractable, "heavy-light" blocks. The results exhibit an initial decay, followed by erratic behavior and recurrences. We also connect this result to gravitational contributions to anomalous dimensions of double trace operators by using the Lorentzian inversion formula to extract the latter. Inverting the stress tensor block provides a pedagogical example of inversion formula machinery.

“…Simons formulation [33,34], for recent discussion see, e.g., [35][36][37][38]. Finally, it is interesting to develop the geodesic Witten diagrams technique by analogy with conformal blocks on the complex plane [10].…”

Section: Jhep06(2016)183mentioning

confidence: 99%

Holographic interpretation of 1-point toroidal block in the semiclassical limit

Alkalaev

Belavin

2016

Abstract:We propose the holographic interpretation of the 1-point conformal block on a torus in the semiclassical regime. To this end we consider the linearized version of the block and find its coefficients by means of the perturbation procedure around natural seed configuration corresponding to the zero-point block. From the AdS/CFT perspective the linearized block is given by the geodesic length of the tadpole graph embedded into the thermal AdS plus the holomorphic part of the thermal AdS action.