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

Abstract

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.

Authors:
ORCiD logo [1];  [2];  [3];  [3]
  1. Univ. of British Columbia, Vancouver, BC (Canada). Dept. of Physics and Astronomy
  2. Cornell Univ., Ithaca, NY (United States). Dept. of Physics
  3. Univ. of Geneva (Switzerland). Dept. of Theoretical Physics
Publication Date:
Research Org.:
Cornell Univ., Ithaca, NY (United States); Univ. of British Columbia, Vancouver, BC (Canada); Univ. of Geneva (Switzerland)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Natural Sciences and Engineering Research Council of Canada (NSERC); Simons Foundation (United States); Swiss National Science Foundation (SNSF)
OSTI Identifier:
1425794
Grant/Contract Number:  
SC0014123; 376206; 200021 162796; NCCR 51NF40-141869
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 9; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTRONOMY AND ASTROPHYSICS; AdS-CFT correspondence; black holes; conformal field theory

Citation Formats

Anous, Tarek, Hartman, Thomas, Rovai, Antonin, and Sonner, Julian. From conformal blocks to path integrals in the Vaidya geometry. United States: N. p., 2017. Web. doi:10.1007/JHEP09(2017)009.
Anous, Tarek, Hartman, Thomas, Rovai, Antonin, & Sonner, Julian. From conformal blocks to path integrals in the Vaidya geometry. United States. doi:10.1007/JHEP09(2017)009.
Anous, Tarek, Hartman, Thomas, Rovai, Antonin, and Sonner, Julian. Mon . "From conformal blocks to path integrals in the Vaidya geometry". United States. doi:10.1007/JHEP09(2017)009. https://www.osti.gov/servlets/purl/1425794.
@article{osti_1425794,
title = {From conformal blocks to path integrals in the Vaidya geometry},
author = {Anous, Tarek and Hartman, Thomas and Rovai, Antonin and Sonner, Julian},
abstractNote = {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.},
doi = {10.1007/JHEP09(2017)009},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2017,
place = {United States},
year = {2017},
month = {9}
}

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Cited by: 6 works
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    Works referencing / citing this record:

    Covariant holographic entanglement negativity for disjoint intervals in $$AdS_3/CFT_2$$ A d S 3 / C F T 2
    journal, June 2019