4D scattering amplitudes and asymptotic symmetries from 2D CFT

Cheung, Clifford; de la Fuente, Anton; Sundrum, Raman

doi:10.1007/JHEP01(2017)112

Title: 4D scattering amplitudes and asymptotic symmetries from 2D CFT

Abstract

We reformulate the scattering amplitudes of 4D at space gauge theory and gravity in the language of a 2D CFT on the celestial sphere. The resulting CFT structure exhibits an OPE constructed from 4D collinear singularities, as well as infinite-dimensional Kac-Moody and Virasoro algebras encoding the asymptotic symmetries of 4D at space. We derive these results by recasting 4D dynamics in terms of a convenient foliation of flat space into 3D Euclidean AdS and Lorentzian dS geometries. Tree-level scattering amplitudes take the form of Witten diagrams for a continuum of (A)dS modes, which are in turn equivalent to CFT correlators via the (A)dS/CFT dictionary. The Ward identities for the 2D conserved currents are dual to 4D soft theorems, while the bulk-boundary propagators of massless (A)dS modes are superpositions of the leading and subleading Weinberg soft factors of gauge theory and gravity. In general, the massless (A)dS modes are 3D Chern-Simons gauge fields describing the soft, single helicity sectors of 4D gauge theory and gravity. Consistent with the topological nature of Chern-Simons theory, Aharonov-Bohm effects record the \tracks" of hard particles in the soft radiation, leading to a simple characterization of gauge and gravitational memories. Soft particle exchanges between hard processesmore »« less

Authors:

Cheung, Clifford ^[1]; de la Fuente, Anton ^[2]; Sundrum, Raman ^[2]

California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
Univ. of Maryland, College Park, MD (United States). Dept. of Physics

Publication Date:: Wed Jan 25 00:00:00 EST 2017

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE; National Science Foundation (NSF)

Contributing Org.:: Univ. of Maryland, College Park, MD (United States)

OSTI Identifier:: 1360787

Grant/Contract Number:: SC0010255; PHY-1315155

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: 1; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Conformal Field Theory; Scattering Amplitudes

Citation Formats


                    Cheung, Clifford, de la Fuente, Anton, and Sundrum, Raman. 4D scattering amplitudes and asymptotic symmetries from 2D CFT.  United States: N. p., 2017. 
Web.  doi:10.1007/JHEP01(2017)112.

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                    Cheung, Clifford, de la Fuente, Anton, & Sundrum, Raman. 4D scattering amplitudes and asymptotic symmetries from 2D CFT.  United States.  https://doi.org/10.1007/JHEP01(2017)112

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                    Cheung, Clifford, de la Fuente, Anton, and Sundrum, Raman. Wed .  
"4D scattering amplitudes and asymptotic symmetries from 2D CFT".  United States.  https://doi.org/10.1007/JHEP01(2017)112.  https://www.osti.gov/servlets/purl/1360787.

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@article{osti_1360787,

  title        = {4D scattering amplitudes and asymptotic symmetries from 2D CFT},

  author       = {Cheung, Clifford and de la Fuente, Anton and Sundrum, Raman},

  abstractNote = {We reformulate the scattering amplitudes of 4D at space gauge theory and gravity in the language of a 2D CFT on the celestial sphere. The resulting CFT structure exhibits an OPE constructed from 4D collinear singularities, as well as infinite-dimensional Kac-Moody and Virasoro algebras encoding the asymptotic symmetries of 4D at space. We derive these results by recasting 4D dynamics in terms of a convenient foliation of flat space into 3D Euclidean AdS and Lorentzian dS geometries. Tree-level scattering amplitudes take the form of Witten diagrams for a continuum of (A)dS modes, which are in turn equivalent to CFT correlators via the (A)dS/CFT dictionary. The Ward identities for the 2D conserved currents are dual to 4D soft theorems, while the bulk-boundary propagators of massless (A)dS modes are superpositions of the leading and subleading Weinberg soft factors of gauge theory and gravity. In general, the massless (A)dS modes are 3D Chern-Simons gauge fields describing the soft, single helicity sectors of 4D gauge theory and gravity. Consistent with the topological nature of Chern-Simons theory, Aharonov-Bohm effects record the \tracks" of hard particles in the soft radiation, leading to a simple characterization of gauge and gravitational memories. Soft particle exchanges between hard processes define the Kac-Moody level and Virasoro central charge, which are thereby related to the 4D gauge coupling and gravitational strength in units of an infrared cutoff. Lastly, we discuss a toy model for black hole horizons via a restriction to the Rindler region.},

  doi          = {10.1007/JHEP01(2017)112},

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

  number       = 1,

  volume       = 2017,

  place        = {United States},

  year         = {Wed Jan 25 00:00:00 EST 2017},

  month        = {Wed Jan 25 00:00:00 EST 2017}

}

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Journal Article Nande, Anjalika ; Pate, Monica ; Strominger, Andrew - Journal of High Energy Physics (Online)

The soft factorization theorem for 4D abelian gauge theory states that the S -matrix factorizes into soft and hard parts, with the universal soft part containing all soft and collinear poles. Similarly, correlation functions on the sphere in a 2D CFT with a U(1) Kac-Moody current algebra factorize into current algebra and non-current algebra factors, with the current algebra factor fully determined by its pole structure. In this paper, we show that these 4D and 2D factorizations are mathematically the same phenomena. The soft ‘t Hooft-Wilson lines and soft photons are realized as a complexified 2D current algebra on the celestial sphere at null infinity. The current algebra level is determined by the cusp anomalous dimension. The associated complex U(1) boson lives on a torus whose modular parameter is τ=more »« less
Cited by 39
https://doi.org/10.1007/jhep02(2018)079

Full Text Available
Approximate symmetries in d = 4 CFTs with an Einstein gravity dual

Journal Article Huang, Kuo-Wei - Journal of High Energy Physics (Online)

By applying the stress-tensor-scalar operator product expansion (OPE) twice, we search for algebraic structures in d = 4 conformal field theories (CFTs) with a pure Einstein gravity dual. We find that a rescaled mode operator defined by an integral of the stress tensor T⁺⁺ on a d = 2 plane satisfies a Virasoro-like algebra when the dimension of the scalar is large. The structure is enhanced to include a Kac-Moody-type algebra if we incorporate the T^-- component. In our scheme, the central terms are finite. It remains challenging to directly compute the stress-tensor sector of d = 4 scalar four-point functions at large central charge, which, based on holography and bootstrap methods, were recently shown to have a Virasoro/more »« less
https://doi.org/10.1007/jhep09(2022)053

Full Text Available

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Title: 4D scattering amplitudes and asymptotic symmetries from 2D CFT

Abstract

Citation Formats

Perturbative Gauge Theory as a String Theory in Twistor Space journal, October 2004

Asymptotic symmetries of QED and Weinberg’s soft photon theorem journal, July 2015

On BMS invariance of gravitational scattering journal, July 2014

Asymptotic symmetries of Yang-Mills theory journal, July 2014

Gravitational memory, BMS supertranslations and soft theorems journal, January 2016

Gauge theory correlators from non-critical string theory journal, May 1998

An electromagnetic analogue of gravitational wave memory journal, September 2013

Constraining conformal field theories with a slightly broken higher spin symmetry journal, May 2013

Significance of Electromagnetic Potentials in the Quantum Theory journal, August 1959

Wave Equations in Conformal Space journal, April 1936

Spinning conformal correlators journal, November 2011

Stability in gauged extended supergravity journal, December 1982

The kinematic algebra from the self-dual sector journal, July 2011

Anti de Sitter space and holography journal, January 1998

New gravitational memories journal, December 2016

Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time journal, October 1962

Extension of the Low Soft-Photon Theorem journal, January 1968

New symmetries of massless QED journal, October 2014

Large N field theories, string theory and gravity journal, January 2000

Self-duality in odd dimensions journal, February 1984

BMS charge algebra journal, December 2011

Remarks on the canonical quantization of the Chern-Simons-Witten theory journal, October 1989

Factorization properties of soft graviton amplitudes journal, May 2011

The dS/CFT correspondence journal, October 2001

Nonabelions in the fractional quantum hall effect journal, August 1991

A relation between tree amplitudes of closed and open strings journal, May 1986

Higher spin realization of the DS/CFT correspondence journal, December 2016

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

Gravitational-wave bursts with memory and experimental prospects journal, May 1987

Non-Abelian statistics in the fractional quantum Hall states journal, February 1991

2D Kac-Moody symmetry of 4D Yang-Mills theory journal, October 2016

The Large-N Limit of Superconformal Field Theories and Supergravity journal, January 1999

A holographic reduction of Minkowski space–time journal, August 2003

Low’s Subleading Soft Theorem as a Symmetry of QED journal, September 2014

Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes journal, November 2012

BMS supertranslations and Weinberg’s soft graviton theorem journal, May 2015

Magnetic Corrections to the Soft Photon Theorem journal, January 2016

Gravitational waves in general relativity, VII. Waves from axi-symmetric isolated system journal, August 1962

A (2+1)-dimensional model for the quantum theory of gravity journal, March 1966

Nonlinear nature of gravitation and gravitational-wave experiments journal, September 1991

Positive energy in anti-de Sitter backgrounds and gauged extended supergravity journal, September 1982

Soft Hair on Black Holes journal, June 2016

Non-gaussian features of primordial fluctuations in single field inflationary models journal, May 2003

Infrared Photons and Gravitons journal, October 1965

BCJ duality and the double copy in the soft limit journal, February 2013

Semiclassical Virasoro symmetry of the quantum gravity S $$ \mathcal{S} $$ -matrix journal, August 2014

A current algebra for some gauge theory amplitudes journal, November 1988

2 + 1 dimensional gravity as an exactly soluble system journal, December 1988

Spinning AdS propagators journal, September 2014

Unitarity and the holographic S-Matrix journal, October 2012

Symmetries of Asymptotically Flat Four-Dimensional Spacetimes at Null Infinity Revisited journal, September 2010

On holomorphic factorization of WZW and coset models journal, February 1992

Bremsstrahlung of Very Low-Energy Quanta in Elementary Particle Collisions journal, May 1958

Soft theorems from effective field theory journal, June 2015

Loop corrections to soft theorems in gauge theories and gravity journal, December 2014

Quantum field theory and the Jones polynomial journal, September 1989

Wave Equations in Conformal Space: Wave Equation for Nucleon journal, January 1955

2D Kac-Moody symmetry of 4D Yang-Mills theory text, January 2016

The Kinematic Algebra From the Self-Dual Sector text, January 2011

BMS charge algebra text, January 2011

Analyticity and the Holographic S-Matrix text, January 2011

Holographic Reconstruction and Renormalization in Asymptotically Ricci-flat Spacetimes text, January 2012

BCJ duality and the double copy in the soft limit text, January 2012

Asymptotic Symmetries of Yang-Mills Theory text, January 2013

On BMS Invariance of Gravitational Scattering text, January 2013

Loop Corrections to Soft Theorems in Gauge Theories and Gravity text, January 2014

Jerusalem Lectures on Black Holes and Quantum Information text, January 2014

Gravitational Memory, BMS Supertranslations and Soft Theorems preprint, January 2014

Soft Theorems from Effective Field Theory preprint, January 2014

2D Kac-Moody Symmetry of 4D Yang-Mills Theory text, January 2015

Magnetic Corrections to the Soft Photon Theorem text, January 2015

Soft Hair on Black Holes text, January 2016

Non-Gaussian features of primordial fluctuations in single field inflationary models text, January 2002

Perturbative Gauge Theory As A String Theory In Twistor Space text, January 2003

Gauge Theory Correlators from Non-Critical String Theory text, January 1998

Anti De Sitter Space And Holography text, January 1998

Large N Field Theories, String Theory and Gravity text, January 1999

Perturbative Gauge Theory as a String Theory in Twistor Space
journal, October 2004

Asymptotic symmetries of QED and Weinberg’s soft photon theorem
journal, July 2015

On BMS invariance of gravitational scattering
journal, July 2014

Asymptotic symmetries of Yang-Mills theory
journal, July 2014

Gravitational memory, BMS supertranslations and soft theorems
journal, January 2016

Gauge theory correlators from non-critical string theory
journal, May 1998

An electromagnetic analogue of gravitational wave memory
journal, September 2013

Constraining conformal field theories with a slightly broken higher spin symmetry
journal, May 2013

Significance of Electromagnetic Potentials in the Quantum Theory
journal, August 1959

Wave Equations in Conformal Space
journal, April 1936

Spinning conformal correlators
journal, November 2011

Stability in gauged extended supergravity
journal, December 1982

The kinematic algebra from the self-dual sector
journal, July 2011

Anti de Sitter space and holography
journal, January 1998

New gravitational memories
journal, December 2016

Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time
journal, October 1962

Extension of the Low Soft-Photon Theorem
journal, January 1968

New symmetries of massless QED
journal, October 2014

Large N field theories, string theory and gravity
journal, January 2000

Self-duality in odd dimensions
journal, February 1984

BMS charge algebra
journal, December 2011

Remarks on the canonical quantization of the Chern-Simons-Witten theory
journal, October 1989

Factorization properties of soft graviton amplitudes
journal, May 2011

The dS/CFT correspondence
journal, October 2001

Nonabelions in the fractional quantum hall effect
journal, August 1991

A relation between tree amplitudes of closed and open strings
journal, May 1986

Higher spin realization of the DS/CFT correspondence
journal, December 2016

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

Gravitational-wave bursts with memory and experimental prospects
journal, May 1987

Non-Abelian statistics in the fractional quantum Hall states
journal, February 1991

2D Kac-Moody symmetry of 4D Yang-Mills theory
journal, October 2016

The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999

A holographic reduction of Minkowski space–time
journal, August 2003

Low’s Subleading Soft Theorem as a Symmetry of QED
journal, September 2014

Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes
journal, November 2012

BMS supertranslations and Weinberg’s soft graviton theorem
journal, May 2015

Magnetic Corrections to the Soft Photon Theorem
journal, January 2016

Gravitational waves in general relativity, VII. Waves from axi-symmetric isolated system
journal, August 1962

A (2+1)-dimensional model for the quantum theory of gravity
journal, March 1966

Nonlinear nature of gravitation and gravitational-wave experiments
journal, September 1991

Positive energy in anti-de Sitter backgrounds and gauged extended supergravity
journal, September 1982

Soft Hair on Black Holes
journal, June 2016

Non-gaussian features of primordial fluctuations in single field inflationary models
journal, May 2003

Infrared Photons and Gravitons
journal, October 1965

BCJ duality and the double copy in the soft limit
journal, February 2013

Semiclassical Virasoro symmetry of the quantum gravity S $$ \mathcal{S} $$ -matrix
journal, August 2014

A current algebra for some gauge theory amplitudes
journal, November 1988

2 + 1 dimensional gravity as an exactly soluble system
journal, December 1988

Spinning AdS propagators
journal, September 2014

Unitarity and the holographic S-Matrix
journal, October 2012

Symmetries of Asymptotically Flat Four-Dimensional Spacetimes at Null Infinity Revisited
journal, September 2010

On holomorphic factorization of WZW and coset models
journal, February 1992

Bremsstrahlung of Very Low-Energy Quanta in Elementary Particle Collisions
journal, May 1958

Soft theorems from effective field theory
journal, June 2015

Loop corrections to soft theorems in gauge theories and gravity
journal, December 2014

Quantum field theory and the Jones polynomial
journal, September 1989

Wave Equations in Conformal Space: Wave Equation for Nucleon
journal, January 1955

2D Kac-Moody symmetry of 4D Yang-Mills theory
text, January 2016

The Kinematic Algebra From the Self-Dual Sector
text, January 2011

BMS charge algebra
text, January 2011

Analyticity and the Holographic S-Matrix
text, January 2011

Holographic Reconstruction and Renormalization in Asymptotically Ricci-flat Spacetimes
text, January 2012

BCJ duality and the double copy in the soft limit
text, January 2012

Asymptotic Symmetries of Yang-Mills Theory
text, January 2013

On BMS Invariance of Gravitational Scattering
text, January 2013

Loop Corrections to Soft Theorems in Gauge Theories and Gravity
text, January 2014

Jerusalem Lectures on Black Holes and Quantum Information
text, January 2014

Gravitational Memory, BMS Supertranslations and Soft Theorems
preprint, January 2014

Soft Theorems from Effective Field Theory
preprint, January 2014

2D Kac-Moody Symmetry of 4D Yang-Mills Theory
text, January 2015

Magnetic Corrections to the Soft Photon Theorem
text, January 2015

Soft Hair on Black Holes
text, January 2016

Non-Gaussian features of primordial fluctuations in single field inflationary models
text, January 2002

Perturbative Gauge Theory As A String Theory In Twistor Space
text, January 2003

Gauge Theory Correlators from Non-Critical String Theory
text, January 1998

Anti De Sitter Space And Holography
text, January 1998

Large N Field Theories, String Theory and Gravity
text, January 1999

Null infinity and unitary representation of the Poincare group
journal, January 2019

On asymptotic symmetries of 3d extended supergravities
journal, February 2019

A d-dimensional stress tensor for Minkd+2 gravity
journal, May 2018