Mellin bootstrap for scalars in generic dimension

Golden, John; Mayerson, Daniel R.

doi:10.1007/jhep06(2018)066

Title: Mellin bootstrap for scalars in generic dimension

Abstract

We use the recently developed framework of the Mellin bootstrap to study perturbatively free scalar CFTs in arbitrary dimensions. This approach uses the crossing-symmetric Mellin space formulation of correlation functions to generate algebraic bootstrap equations by demanding that only physical operators contribute to the OPE. We find that there are no perturbatively interacting CFTs with only fundamental scalars in d > 6 dimensions (to at least second order in the perturbation). Our results can be seen as a modest step towards understanding the space of interacting CFTs in d > 6 and are consistent with the intuition that no such CFTs exist.

Authors:

Golden, John ^[1];

^[1]

Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Physics and Leinweber Center for Theoretical Physics

Publication Date:: Wed Jun 13 00:00:00 EDT 2018

Research Org.:: Univ. of Michigan, Ann Arbor, MI (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1507007

Grant/Contract Number:: FG02-95ER40899

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: 6; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Theory; Field Theories in Higher Dimensions

Citation Formats


                    Golden, John, and Mayerson, Daniel R. Mellin bootstrap for scalars in generic dimension.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep06(2018)066.

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                    Golden, John, & Mayerson, Daniel R. Mellin bootstrap for scalars in generic dimension.  United States.  https://doi.org/10.1007/jhep06(2018)066

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                    Golden, John, and Mayerson, Daniel R. Wed .  
"Mellin bootstrap for scalars in generic dimension".  United States.  https://doi.org/10.1007/jhep06(2018)066.  https://www.osti.gov/servlets/purl/1507007.

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@article{osti_1507007,

  title        = {Mellin bootstrap for scalars in generic dimension},

  author       = {Golden, John and Mayerson, Daniel R.},

  abstractNote = {We use the recently developed framework of the Mellin bootstrap to study perturbatively free scalar CFTs in arbitrary dimensions. This approach uses the crossing-symmetric Mellin space formulation of correlation functions to generate algebraic bootstrap equations by demanding that only physical operators contribute to the OPE. We find that there are no perturbatively interacting CFTs with only fundamental scalars in d > 6 dimensions (to at least second order in the perturbation). Our results can be seen as a modest step towards understanding the space of interacting CFTs in d > 6 and are consistent with the intuition that no such CFTs exist.},

  doi          = {10.1007/jhep06(2018)066},

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

  number       = 6,

  volume       = 2018,

  place        = {United States},

  year         = {Wed Jun 13 00:00:00 EDT 2018},

  month        = {Wed Jun 13 00:00:00 EDT 2018}

}

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Works referenced in this record:

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Rattazzi, Riccardo; Rychkov, Vyacheslav S.; Tonni, Erik
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Costa, Miguel S.; Goncalves, Vasco; Penedones, João
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Gliozzi, Ferdinando; Guerrieri, Andrea L.; Petkou, Anastasios C.
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journal, June 2016

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Writing CFT correlation functions as AdS scattering amplitudes
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Penedones, Joao
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Works referencing / citing this record:

On Mellin amplitudes in SCFTs with eight supercharges
journal, July 2018

Zhou, Xinan
Journal of High Energy Physics, Vol. 2018, Issue 7
DOI: 10.1007/jhep07(2018)147

Scalar CFTs and Their Large N Limits
text, January 2017

Rong, Junchen; Su, Ning
arXiv
DOI: 10.48550/arxiv.1712.00985

On Mellin Amplitudes in SCFTs with Eight Supercharges
text, January 2018

Zhou, Xinan
arXiv
DOI: 10.48550/arxiv.1804.02397

Scalar CFTs and their large N limits
journal, September 2018

Rong, Junchen; Su, Ning
Journal of High Energy Physics, Vol. 2018, Issue 9
DOI: 10.1007/jhep09(2018)103

On the Polyakov-Mellin bootstrap
journal, December 2018

Gopakumar, Rajesh; Sinha, Aninda
Journal of High Energy Physics, Vol. 2018, Issue 12
DOI: 10.1007/jhep12(2018)040

Crossing symmetry, transcendentality and the Regge behaviour of 1d CFTs
journal, July 2020

Ferrero, Pietro; Ghosh, Kausik; Sinha, Aninda
Journal of High Energy Physics, Vol. 2020, Issue 7
DOI: 10.1007/jhep07(2020)170

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Title: Mellin bootstrap for scalars in generic dimension

Abstract

Citation Formats

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

Generalized Wilson-Fisher Critical Points from the Conformal Operator Product Expansion journal, February 2017

Simplifying large spin bootstrap in Mellin space journal, January 2018

All unitary ray representations of the conformal group SU(2,2) with positive energy journal, February 1977

Conformal Bootstrap in Mellin Space journal, February 2017

The Conformal Bootstrap conference, January 2017

Towards a bootstrap approach to higher orders of epsilon expansion journal, February 2018

Conformal Regge theory journal, December 2012

The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points journal, April 2017

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

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Solving the 3D Ising model with the conformal bootstrap journal, July 2012

The conformal bootstrap journal, June 2016

A Mellin space approach to the conformal bootstrap journal, May 2017

Writing CFT correlation functions as AdS scattering amplitudes journal, March 2011

Mellin space bootstrap for global symmetry journal, July 2017

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

On Mellin amplitudes in SCFTs with eight supercharges journal, July 2018

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Scalar CFTs and their large N limits journal, September 2018

On the Polyakov-Mellin bootstrap journal, December 2018

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

Generalized Wilson-Fisher Critical Points from the Conformal Operator Product Expansion
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Simplifying large spin bootstrap in Mellin space
journal, January 2018

All unitary ray representations of the conformal group SU(2,2) with positive energy
journal, February 1977

Conformal Bootstrap in Mellin Space
journal, February 2017

The Conformal Bootstrap
conference, January 2017

Towards a bootstrap approach to higher orders of epsilon expansion
journal, February 2018

Conformal Regge theory
journal, December 2012

The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points
journal, April 2017

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

Supersymmetries and their representations
journal, March 1978

Solving the 3D Ising model with the conformal bootstrap
journal, July 2012

The conformal bootstrap
journal, June 2016

A Mellin space approach to the conformal bootstrap
journal, May 2017

Writing CFT correlation functions as AdS scattering amplitudes
journal, March 2011

Mellin space bootstrap for global symmetry
journal, July 2017

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

On Mellin amplitudes in SCFTs with eight supercharges
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Scalar CFTs and Their Large N Limits
text, January 2017

On Mellin Amplitudes in SCFTs with Eight Supercharges
text, January 2018

Scalar CFTs and their large N limits
journal, September 2018

On the Polyakov-Mellin bootstrap
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Crossing symmetry, transcendentality and the Regge behaviour of 1d CFTs
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