From conformal blocks to path integrals in the Vaidya geometry

Anous, Tarek; Hartman, Thomas; Rovai, Antonin; Sonner, Julian

doi:10.1007/JHEP09(2017)009

Title: From conformal blocks to path integrals in the Vaidya geometry

Journal Article · Mon Sep 04 00:00:00 EDT 2017 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP09(2017)009· OSTI ID:1425794

^[1]; Hartman, Thomas ^[2]; Rovai, Antonin ^[3]; Sonner, Julian ^[3]

Univ. of British Columbia, Vancouver, BC (Canada). Dept. of Physics and Astronomy
Cornell Univ., Ithaca, NY (United States). Dept. of Physics
Univ. of Geneva (Switzerland). Dept. of Theoretical Physics

Correlators in conformal field theory are naturally organized as a sum over conformal blocks. In holographic theories, this sum must reorganize into a path integral over bulk fields and geometries. We explore how these two sums are related in the case of a point particle moving in the background of a 3d collapsing black hole. The conformal block expansion is recast as a sum over paths of the first-quantized particle moving in the bulk geometry. Off-shell worldlines of the particle correspond to subdominant contributions in the Euclidean conformal block expansion, but these same operators must be included in order to correctly reproduce complex saddles in the Lorentzian theory. During thermalization, a complex saddle dominates under certain circumstances; in this case, the CFT correlator is not given by the Virasoro identity block in any channel, but can be recovered by summing heavy operators. This effectively converts the conformal block expansion in CFT from a sum over intermediate states to a sum over channels that mimics the bulk path integral.

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Research Organization:: Cornell Univ., Ithaca, NY (United States); Univ. of British Columbia, Vancouver, BC (Canada); Univ. of Geneva (Switzerland)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); Natural Sciences and Engineering Research Council of Canada (NSERC); Simons Foundation (United States); Swiss National Science Foundation (SNSF)

Grant/Contract Number:: SC0014123; 376206; 200021 162796; NCCR 51NF40-141869

OSTI ID:: 1425794

Journal Information:: Journal of High Energy Physics (Online), Vol. 2017, Issue 9; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 21 works

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Superluminal chaos after a quantum quench Balasubramanian, Vijay; Craps, Ben; De Clerck, Marine Journal of High Energy Physics, Vol. 2019, Issue 12 https://doi.org/10.1007/jhep12(2019)132	journal	December 2019
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