Witten diagrams revisited: the AdS geometry of conformal blocks

Hijano, Eliot; Kraus, Per; Perlmutter, Eric; Snively, River

doi:10.1007/JHEP01(2016)146

Title: Witten diagrams revisited: the AdS geometry of conformal blocks

Journal Article · Mon Jan 25 00:00:00 EST 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP01(2016)146· OSTI ID:1327296

Hijano, Eliot ^[1]; Kraus, Per ^[1]; Perlmutter, Eric ^[2]; Snively, River ^[1]

Univ. of California, Los Angeles, CA (United States). Dept. of Physics and Astronomy
Princeton Univ., NJ (United States). Dept. of Physics

Here, we develop a new method for decomposing blocks. The steps involved are elementary, requiring no explicit integration, and operate directly in position space. Central to this construction is an appealingly simple answer to the question: what object in AdS computes a conformal block? The answer is a "geodesic Witten diagram", which is essentially an ordinary exchange Witten diagram, except that the cubic vertices are not integrated over all of AdS, but only over bulk geodesics connecting the boundary operators. In particular, we also consider the case of four-point functions of scalar operators, and show how to easily reproduce existing results for the relevant conformal blocks in arbitrary dimension.

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Research Organization:: Princeton Univ., NJ (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-91ER40671; NSF PHY11-25915; PHY-1313986

OSTI ID:: 1327296

Journal Information:: Journal of High Energy Physics (Online), Vol. 2016, Issue 1; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 134 works

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Weight Shifting Operators and Conformal Blocks Karateev, Denis; Kravchuk, Petr; Simmons-Duffin, David arXiv https://doi.org/10.48550/arxiv.1706.07813	text	January 2017
Kinematic space for conical defects Cresswell, Jesse C.; Peet, Amanda W. arXiv https://doi.org/10.48550/arxiv.1708.09838	text	January 2017
Bands and gaps in Nekrasov partition function Gorsky, A.; Milekhin, A.; Sopenko, N. arXiv https://doi.org/10.48550/arxiv.1712.02936	text	January 2017
Double-Trace Deformations of Conformal Correlations Giombi, Simone; Kirilin, Vladimir; Perlmutter, Eric arXiv https://doi.org/10.48550/arxiv.1801.01477	text	January 2018
The Conformal Bootstrap at Finite Temperature Iliesiu, Luca; Koloğlu, Murat; Mahajan, Raghu arXiv https://doi.org/10.48550/arxiv.1802.10266	text	January 2018
Towards Entanglement of Purification for Conformal Field Theories Hirai, Hayato; Tamaoka, Kotaro; Yokoya, Tsuyoshi arXiv https://doi.org/10.48550/arxiv.1803.10539	text	January 2018
Fermions in Geodesic Witten Diagrams Nishida, Mitsuhiro; Tamaoka, Kotaro arXiv https://doi.org/10.48550/arxiv.1805.00217	text	January 2018
A Conformal Collider for Holographic CFTs Afkhami-Jeddi, Nima; Kundu, Sandipan; Tajdini, Amirhossein arXiv https://doi.org/10.48550/arxiv.1805.07393	text	January 2018
Large $c$ Virasoro Blocks from Monodromy Method beyond Known Limits Kusuki, Yuya arXiv https://doi.org/10.48550/arxiv.1806.04352	text	January 2018
Holographic relations for OPE blocks in excited states Cresswell, Jesse C.; Jardine, Ian T.; Peet, Amanda W. arXiv https://doi.org/10.48550/arxiv.1809.09107	text	January 2018
An Analytic Approach to BCFT$_d$ Mazáč, Dalimil; Rastelli, Leonardo; Zhou, Xinan arXiv https://doi.org/10.48550/arxiv.1812.09314	text	January 2018
Holographic dual of the five-point conformal block Parikh, Sarthak arXiv https://doi.org/10.48550/arxiv.1901.01267	text	January 2019
Structure Constants from Modularity in Warped CFT Song, Wei; Xu, Jianfei arXiv https://doi.org/10.48550/arxiv.1903.01346	text	January 2019
Dynamical Constraints on RG Flows and Cosmology Baumann, Daniel; Green, Daniel; Hartman, Thomas arXiv https://doi.org/10.48550/arxiv.1906.10226	text	January 2019
Towards the higher point holographic momentum space amplitudes II: Gravitons Albayrak, Soner; Kharel, Savan arXiv https://doi.org/10.48550/arxiv.1908.01835	text	January 2019

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