Conformal differential operator in embedding space and its applications

Fortin, Jean-François; Skiba, Witold

doi:10.1007/jhep07(2019)093

Title: Conformal differential operator in embedding space and its applications

Abstract

We develop techniques useful for obtaining conformal blocks in embedding space. We construct a unique differential operator in embedding space and use it to construct a function that will be an important ingredient in assembling conformal blocks. We show a number of relations that the components of conformal blocks satisfy and find invariance of our expressions under the dihedral group.

Authors:

Fortin, Jean-François ^[1]; Skiba, Witold ^[2]

Univ. Laval, Qubec, QC (Canada)
Yale Univ., New Haven, CT (United States)

Publication Date:: Wed Jul 17 00:00:00 EDT 2019

Research Org.:: Yale Univ., New Haven, CT (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1610196

Grant/Contract Number:: FG02-92ER40704

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: 2019; Journal Issue: 7; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; Conformal Field Theory; Conformal and W Symmetry

Citation Formats


                    Fortin, Jean-François, and Skiba, Witold. Conformal differential operator in embedding space and its applications.  United States: N. p., 2019. 
Web.  doi:10.1007/jhep07(2019)093.

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                    Fortin, Jean-François, & Skiba, Witold. Conformal differential operator in embedding space and its applications.  United States.  https://doi.org/10.1007/jhep07(2019)093

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                    Fortin, Jean-François, and Skiba, Witold. Wed .  
"Conformal differential operator in embedding space and its applications".  United States.  https://doi.org/10.1007/jhep07(2019)093.  https://www.osti.gov/servlets/purl/1610196.

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@article{osti_1610196,

  title        = {Conformal differential operator in embedding space and its applications},

  author       = {Fortin, Jean-François and Skiba, Witold},

  abstractNote = {We develop techniques useful for obtaining conformal blocks in embedding space. We construct a unique differential operator in embedding space and use it to construct a function that will be an important ingredient in assembling conformal blocks. We show a number of relations that the components of conformal blocks satisfy and find invariance of our expressions under the dihedral group.},

  doi          = {10.1007/jhep07(2019)093},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 7,

  volume       = 2019,

  place        = {United States},

  year         = {Wed Jul 17 00:00:00 EDT 2019},

  month        = {Wed Jul 17 00:00:00 EDT 2019}

}

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Works referenced in this record:

Finite-component field representations of the conformal group
journal, June 1969

Mack, G.; Salam, Abdus
Annals of Physics, Vol. 53, Issue 1
DOI: 10.1016/0003-4916(69)90278-4

Bounding scalar operator dimensions in 4 D CFT
journal, December 2008

Rattazzi, Riccardo; Rychkov, Vyacheslav S.; Tonni, Erik
Journal of High Energy Physics, Vol. 2008, Issue 12
DOI: 10.1088/1126-6708/2008/12/031

Scalar-vector bootstrap
journal, January 2016

Rejon-Barrera, Fernando; Robbins, Daniel
Journal of High Energy Physics, Vol. 2016, Issue 1
DOI: 10.1007/JHEP01(2016)139

Recursion relations for conformal blocks
journal, September 2016

Penedones, João; Trevisani, Emilio; Yamazaki, Masahito
Journal of High Energy Physics, Vol. 2016, Issue 9
DOI: 10.1007/JHEP09(2016)070

Projectors and seed conformal blocks for traceless mixed-symmetry tensors
journal, July 2016

Costa, Miguel S.; Hansen, Tobias; Penedones, João
Journal of High Energy Physics, Vol. 2016, Issue 7
DOI: 10.1007/JHEP07(2016)018

Seed conformal blocks in 4D CFT
journal, February 2016

Echeverri, Alejandro Castedo; Elkhidir, Emtinan; Karateev, Denis
Journal of High Energy Physics, Vol. 2016, Issue 2
DOI: 10.1007/JHEP02(2016)183

Harmony of spinning conformal blocks
journal, March 2017

Schomerus, Volker; Sobko, Evgeny; Isachenkov, Mikhail
Journal of High Energy Physics, Vol. 2017, Issue 3
DOI: 10.1007/JHEP03(2017)085

Higher symmetries of the Laplacian
journal, January 2005

Eastwood, Michael
Annals of Mathematics, Vol. 161, Issue 3
DOI: 10.4007/annals.2005.161.1645

Spinning conformal blocks
journal, November 2011

Costa, Miguel S.; Penedones, João; Poland, David
Journal of High Energy Physics, Vol. 2011, Issue 11
DOI: 10.1007/JHEP11(2011)154

Tensor representations of conformal algebra and conformally covariant operator product expansion
journal, March 1973

Ferrara, S.; Grillo, A. F.; Gatto, R.
Annals of Physics, Vol. 76, Issue 1
DOI: 10.1016/0003-4916(73)90446-6

Thomas's Structure Bundle for Conformal, Projective and Related Structures
journal, December 1994

Bailey, T. N.; Eastwood, M. G.; Gover, A. R.
Rocky Mountain Journal of Mathematics, Vol. 24, Issue 4
DOI: 10.1216/rmjm/1181072333

Bootstrapping mixed correlators in the 3D Ising model
journal, November 2014

Kos, Filip; Poland, David; Simmons-Duffin, David
Journal of High Energy Physics, Vol. 2014, Issue 11
DOI: 10.1007/JHEP11(2014)109

Convergence of operator product expansions on the vacuum in conformal invariant quantum field theory
journal, June 1977

Mack, G.
Communications in Mathematical Physics, Vol. 53, Issue 2
DOI: 10.1007/BF01609130

Conformal four point functions and the operator product expansion
journal, April 2001

Dolan, F. A.; Osborn, H.
Nuclear Physics B, Vol. 599, Issue 1-2
DOI: 10.1016/S0550-3213(01)00013-X

Conformal partial waves and the operator product expansion
journal, February 2004

Dolan, F. A.; Osborn, H.
Nuclear Physics B, Vol. 678, Issue 1-2
DOI: 10.1016/j.nuclphysb.2003.11.016

Conformal correlators of mixed-symmetry tensors
journal, February 2015

Costa, Miguel S.; Hansen, Tobias
Journal of High Energy Physics, Vol. 2015, Issue 2
DOI: 10.1007/JHEP02(2015)151

Wave Equations in Conformal Space
journal, April 1936

Dirac, P. A. M.
The Annals of Mathematics, Vol. 37, Issue 2
DOI: 10.2307/1968455

Superintegrability of $d$ -Dimensional Conformal Blocks
journal, August 2016

Isachenkov, Mikhail; Schomerus, Volker
Physical Review Letters, Vol. 117, Issue 7
DOI: 10.1103/PhysRevLett.117.071602

Conformal invariance on the light cone and canonical dimensions
journal, November 1971

Ferrara, S.; Gatto, R.; Grillo, A. F.
Nuclear Physics B, Vol. 34, Issue 2
DOI: 10.1016/0550-3213(71)90333-6

Spinning conformal correlators
journal, November 2011

Costa, Miguel S.; Penedones, João; Poland, David
Journal of High Energy Physics, Vol. 2011, Issue 11
DOI: 10.1007/JHEP11(2011)071

Manifestly conformal covariant operator-product expansion
journal, December 1971

Ferrara, S.; Grillo, A. F.; Gatto, R.
Lettere Al Nuovo Cimento Series 2, Vol. 2, Issue 26
DOI: 10.1007/BF02770435

On the system of partial differential equations associated with Appell's function F₄
journal, February 1995

Exton, H.
Journal of Physics A: Mathematical and General, Vol. 28, Issue 3
DOI: 10.1088/0305-4470/28/3/017

Conformal Invariance on the Light cone and Canonical Dimensions
text, January 1971

Ferrara, S.; Gatto, R.; Grillo, A. F.
INFN Open Access Repository
DOI: 10.15161/oar.it/1448902392.29

Wave Equations in Conformal Space
journal, April 1936

Dirac, P. A. M.
The Annals of Mathematics, Vol. 37, Issue 2
DOI: 10.2307/1968455

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Title: Conformal differential operator in embedding space and its applications

Abstract

Citation Formats

Finite-component field representations of the conformal group journal, June 1969

Bounding scalar operator dimensions in 4 D CFT journal, December 2008

Scalar-vector bootstrap journal, January 2016

Recursion relations for conformal blocks journal, September 2016

Projectors and seed conformal blocks for traceless mixed-symmetry tensors journal, July 2016

Seed conformal blocks in 4D CFT journal, February 2016

Harmony of spinning conformal blocks journal, March 2017

Higher symmetries of the Laplacian journal, January 2005

Spinning conformal blocks journal, November 2011

Tensor representations of conformal algebra and conformally covariant operator product expansion journal, March 1973

Thomas's Structure Bundle for Conformal, Projective and Related Structures journal, December 1994

Bootstrapping mixed correlators in the 3D Ising model journal, November 2014

Convergence of operator product expansions on the vacuum in conformal invariant quantum field theory journal, June 1977

Conformal four point functions and the operator product expansion journal, April 2001

Conformal partial waves and the operator product expansion journal, February 2004

Conformal correlators of mixed-symmetry tensors journal, February 2015

Wave Equations in Conformal Space journal, April 1936

Superintegrability of d -Dimensional Conformal Blocks journal, August 2016

Conformal invariance on the light cone and canonical dimensions journal, November 1971

Spinning conformal correlators journal, November 2011

Manifestly conformal covariant operator-product expansion journal, December 1971

On the system of partial differential equations associated with Appell's function F4 journal, February 1995

Conformal Invariance on the Light cone and Canonical Dimensions text, January 1971

Wave Equations in Conformal Space journal, April 1936

Finite-component field representations of the conformal group
journal, June 1969

Bounding scalar operator dimensions in 4 D CFT
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Scalar-vector bootstrap
journal, January 2016

Recursion relations for conformal blocks
journal, September 2016

Projectors and seed conformal blocks for traceless mixed-symmetry tensors
journal, July 2016

Seed conformal blocks in 4D CFT
journal, February 2016

Harmony of spinning conformal blocks
journal, March 2017

Higher symmetries of the Laplacian
journal, January 2005

Spinning conformal blocks
journal, November 2011

Tensor representations of conformal algebra and conformally covariant operator product expansion
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Thomas's Structure Bundle for Conformal, Projective and Related Structures
journal, December 1994

Bootstrapping mixed correlators in the 3D Ising model
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Convergence of operator product expansions on the vacuum in conformal invariant quantum field theory
journal, June 1977

Conformal four point functions and the operator product expansion
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Conformal partial waves and the operator product expansion
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Conformal correlators of mixed-symmetry tensors
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Superintegrability of $d$ -Dimensional Conformal Blocks
journal, August 2016

Conformal invariance on the light cone and canonical dimensions
journal, November 1971

Spinning conformal correlators
journal, November 2011

Manifestly conformal covariant operator-product expansion
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On the system of partial differential equations associated with Appell's function F₄
journal, February 1995

Conformal Invariance on the Light cone and Canonical Dimensions
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Wave Equations in Conformal Space
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