The AdS_{3} propagator and the fate of locality
Abstract
We recently used Virasoro symmetry considerations to propose an exact formula for a bulk protofield φ in AdS_{3}. In this paper we study the propagator <φφ>. We show that many techniques from the study of conformal blocks can be generalized to compute it, including the semiclassical monodromy method and both forms of the Zamolodchikov recursion relations. When the results from recursion are expanded at large central charge, they match gravitational perturbation theory for a free scalar field coupled to gravity in our chosen gauge. We find that although the propagator is finite and welldefined at long distances, its perturbative expansion in ${G}_{N}=\frac{3}{2c}$ exhibits UV/IR mixing effects. If we nevertheless interpret <φφ> as a probe of bulk locality, then when ${G}_{N{m}_{\varphi}}\ll 1$ locality breaks down at the new shortdistance scale ${\sigma}_{\ast}\sim \sqrt[4]{{G}_{N}{R}_{\mathrm{A}\mathrm{d}\mathrm{S}}^{3}}$. For φ with very large bulk mass, or at small central charge, bulk locality fails at the AdS length scale. In all cases, locality ‘breakdown’ manifests as singularities or branch cuts at spacelike separation arising from nonperturbative quantum gravitational effects.
 Authors:

 Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Physics and Astronomy
 Boston Univ., MA (United States). Dept. of Physics
 Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Physics and Astronomy; Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP); Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics
 Publication Date:
 Research Org.:
 Boston Univ., MA (United States); Johns Hopkins Univ., Baltimore, MD (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)
 OSTI Identifier:
 1501934
 Grant/Contract Number:
 SC0010025; PHY1454083
 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: 2018; Journal Issue: 4; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdSCFT correspondence; conformal and W Symmetry; conformal field theory; models of quantum gravity
Citation Formats
Chen, Hongbin, Fitzpatrick, A. Liam, Kaplan, Jared, and Li, Daliang. The AdS3 propagator and the fate of locality. United States: N. p., 2018.
Web. doi:10.1007/jhep04(2018)075.
Chen, Hongbin, Fitzpatrick, A. Liam, Kaplan, Jared, & Li, Daliang. The AdS3 propagator and the fate of locality. United States. https://doi.org/10.1007/jhep04(2018)075
Chen, Hongbin, Fitzpatrick, A. Liam, Kaplan, Jared, and Li, Daliang. Fri .
"The AdS3 propagator and the fate of locality". United States. https://doi.org/10.1007/jhep04(2018)075. https://www.osti.gov/servlets/purl/1501934.
@article{osti_1501934,
title = {The AdS3 propagator and the fate of locality},
author = {Chen, Hongbin and Fitzpatrick, A. Liam and Kaplan, Jared and Li, Daliang},
abstractNote = {We recently used Virasoro symmetry considerations to propose an exact formula for a bulk protofield φ in AdS3. In this paper we study the propagator <φφ>. We show that many techniques from the study of conformal blocks can be generalized to compute it, including the semiclassical monodromy method and both forms of the Zamolodchikov recursion relations. When the results from recursion are expanded at large central charge, they match gravitational perturbation theory for a free scalar field coupled to gravity in our chosen gauge. We find that although the propagator is finite and welldefined at long distances, its perturbative expansion in G N = 3 2 c exhibits UV/IR mixing effects. If we nevertheless interpret <φφ> as a probe of bulk locality, then when G N m ϕ ≪ 1 locality breaks down at the new shortdistance scale σ ∗ ∼ G N R A d S 3 4 . For φ with very large bulk mass, or at small central charge, bulk locality fails at the AdS length scale. In all cases, locality ‘breakdown’ manifests as singularities or branch cuts at spacelike separation arising from nonperturbative quantum gravitational effects.},
doi = {10.1007/jhep04(2018)075},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2018,
place = {United States},
year = {2018},
month = {4}
}
Web of Science
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