Soft factorization in QED from 2D Kac-Moody symmetry

Nande, Anjalika; Pate, Monica; Strominger, Andrew

doi:10.1007/jhep02(2018)079

Title: Soft factorization in QED from 2D Kac-Moody symmetry

Abstract

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=$$\frac{2πi}{e^2}$$ + $$\frac{θ}{2π}$$. The correlators of this 2D current algebra fully reproduce the known soft part of the 4D S -matrix, as well as a conjectured generalization involving magnetic charges.

Authors:

Nande, Anjalika ^[1];

^[1]; Strominger, Andrew ^[1]

Harvard Univ., Cambridge, MA (United States). Dept. of Physics

Publication Date:: Wed Feb 14 00:00:00 EST 2018

Research Org.:: Harvard Univ., Cambridge, MA (United States)

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

OSTI Identifier:: 1505226

Grant/Contract Number:: SC0007870

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: 2; 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; Gauge Symmetry; Scattering Amplitudes

Citation Formats


                    Nande, Anjalika, Pate, Monica, and Strominger, Andrew. Soft factorization in QED from 2D Kac-Moody symmetry.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep02(2018)079.

Copy to clipboard


                    Nande, Anjalika, Pate, Monica, & Strominger, Andrew. Soft factorization in QED from 2D Kac-Moody symmetry.  United States.  https://doi.org/10.1007/jhep02(2018)079

Copy to clipboard


                    Nande, Anjalika, Pate, Monica, and Strominger, Andrew. Wed .  
"Soft factorization in QED from 2D Kac-Moody symmetry".  United States.  https://doi.org/10.1007/jhep02(2018)079.  https://www.osti.gov/servlets/purl/1505226.

Copy to clipboard


                    
@article{osti_1505226,

  title        = {Soft factorization in QED from 2D Kac-Moody symmetry},

  author       = {Nande, Anjalika and Pate, Monica and Strominger, Andrew},

  abstractNote = {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=$\frac{2πi}{e^2}$ + $\frac{θ}{2π}$. The correlators of this 2D current algebra fully reproduce the known soft part of the 4D S -matrix, as well as a conjectured generalization involving magnetic charges.},

  doi          = {10.1007/jhep02(2018)079},

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

  number       = 2,

  volume       = 2018,

  place        = {United States},

  year         = {Wed Feb 14 00:00:00 EST 2018},

  month        = {Wed Feb 14 00:00:00 EST 2018}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1007/jhep02(2018)079

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 39 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

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

Campiglia, Miguel; Laddha, Alok
Journal of High Energy Physics, Vol. 2015, Issue 7
DOI: 10.1007/JHEP07(2015)115

S-Duality and Helicity Amplitudes
text, January 2015

Colwell, Kitran; Terning, John
arXiv
DOI: 10.48550/arxiv.1510.07627

Asymptotic symmetries of Yang-Mills theory
journal, July 2014

Strominger, Andrew
Journal of High Energy Physics, Vol. 2014, Issue 7
DOI: 10.1007/JHEP07(2014)151

A note on asymptotic symmetries and soft-photon theorem
text, January 2014

Mohd, Arif
arXiv
DOI: 10.48550/arxiv.1412.5365

Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
text, January 2017

Pasterski, Sabrina; Shao, Shu-Heng; Strominger, Andrew
arXiv
DOI: 10.48550/arxiv.1701.00049

4D scattering amplitudes and asymptotic symmetries from 2D CFT
journal, January 2017

Cheung, Clifford; de la Fuente, Anton; Sundrum, Raman
Journal of High Energy Physics, Vol. 2017, Issue 1
DOI: 10.1007/JHEP01(2017)112

Asymptotic Symmetries of Yang-Mills Theory
text, January 2013

Strominger, Andrew
arXiv
DOI: 10.48550/arxiv.1308.0589

Jet structure and infrared sensitive quantities in perturbative QCD
journal, November 1983

Bassetto, A.; Ciafaloni, M.; Marchesini, G.
Physics Reports, Vol. 100, Issue 4
DOI: 10.1016/0370-1573(83)90083-2

Infrared divergences in QED revisited
journal, October 2017

Kapec, Daniel; Perry, Malcolm; Raclariu, Ana-Maria
Physical Review D, Vol. 96, Issue 8
DOI: 10.1103/PhysRevD.96.085002

Magnetic Corrections to the Soft Photon Theorem
text, January 2015

Strominger, Andrew
arXiv
DOI: 10.48550/arxiv.1509.00543

New symmetries of massless QED
journal, October 2014

He, Temple; Mitra, Prahar; Porfyriadis, Achilleas P.
Journal of High Energy Physics, Vol. 2014, Issue 10
DOI: 10.1007/JHEP10(2014)112

Projectors, Shadows, and Conformal Blocks
text, January 2012

Simmons-Duffin, David
arXiv
DOI: 10.48550/arxiv.1204.3894

Remarks on Asymptotic Symmetries and the Sub-leading Soft Photon Theorem
text, January 2016

Conde, Eduardo; Mao, Pujian
arXiv
DOI: 10.48550/arxiv.1605.09731

Infrared divergences in QED revisited
text, January 2017

Kapec, Daniel; Perry, Malcolm; Raclariu, Ana-Maria
Apollo - University of Cambridge Repository
DOI: 10.17863/cam.62215

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

He, Temple; Mitra, Prahar; Strominger, Andrew
Apollo - University of Cambridge Repository
DOI: 10.17863/cam.58713

Infrared Divergences in QED, Revisited
text, January 2017

Kapec, Daniel; Perry, Malcolm; Raclariu, Ana-Maria
arXiv
DOI: 10.48550/arxiv.1705.04311

Null to time-like infinity Green's functions for asymptotic symmetries in Minkowski spacetime
text, January 2015

Campiglia, Miguel
arXiv
DOI: 10.48550/arxiv.1509.01408

Noether’s second theorem and Ward identities for gauge symmetries
journal, February 2016

Avery, Steven G.; Schwab, Burkhard U. W.
Journal of High Energy Physics, Vol. 2016, Issue 2
DOI: 10.1007/JHEP02(2016)031

4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
text, January 2016

Cheung, Clifford; de la Fuente, Anton; Sundrum, Raman
arXiv
DOI: 10.48550/arxiv.1609.00732

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

He, Temple; Mitra, Prahar; Strominger, Andrew
Journal of High Energy Physics, Vol. 2016, Issue 10
DOI: 10.1007/JHEP10(2016)137

4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
text, January 2016

Cheung, Clifford; de la Fuente, Anton; Sundrum, Raman
arXiv
DOI: 10.48550/arxiv.1609.00732

Magnetic Corrections to the Soft Photon Theorem
journal, January 2016

Strominger, Andrew
Physical Review Letters, Vol. 116, Issue 3
DOI: 10.1103/PhysRevLett.116.031602

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

He, Temple; Mitra, Prahar; Strominger, Andrew
arXiv
DOI: 10.48550/arxiv.1503.02663

Noether's Second Theorem and Ward Identities for Gauge Symmetries
text, January 2015

Avery, Steven G.; Schwab, Burkhard U. W.
arXiv
DOI: 10.48550/arxiv.1510.07038

Infrared Photons and Gravitons
journal, October 1965

Weinberg, Steven
Physical Review, Vol. 140, Issue 2B
DOI: 10.1103/PhysRev.140.B516

Flat space amplitudes and conformal symmetry of the celestial sphere
journal, September 2017

Pasterski, Sabrina; Shao, Shu-Heng; Strominger, Andrew
Physical Review D, Vol. 96, Issue 6
DOI: 10.1103/PhysRevD.96.065026

Subleading soft photons and large gauge transformations
journal, November 2016

Campiglia, Miguel; Laddha, Alok
Journal of High Energy Physics, Vol. 2016, Issue 11
DOI: 10.1007/JHEP11(2016)012

Projectors, shadows, and conformal blocks
journal, April 2014

Simmons-Duffin, David
Journal of High Energy Physics, Vol. 2014, Issue 4
DOI: 10.1007/JHEP04(2014)146

Hard-soft-collinear factorization to all orders
journal, November 2014

Feige, Ilya; Schwartz, Matthew D.
Physical Review D, Vol. 90, Issue 10
DOI: 10.1103/PhysRevD.90.105020

Scattering of Light of Very Low Frequency by Systems of Spin ½
journal, December 1954

Low, F. E.
Physical Review, Vol. 96, Issue 5
DOI: 10.1103/PhysRev.96.1428

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

Low, F. E.
Physical Review, Vol. 110, Issue 4
DOI: 10.1103/PhysRev.110.974

Renormalization of the Wilson loops beyond the leading order
journal, January 1987

Korchemsky, G. P.; Radyushkin, A. V.
Nuclear Physics B, Vol. 283
DOI: 10.1016/0550-3213(87)90277-X

Works referencing / citing this record:

A $d$-Dimensional Stress Tensor for Mink$_{d+2}$ Gravity
text, January 2017

Kapec, Daniel; Mitra, Prahar
arXiv
DOI: 10.48550/arxiv.1711.04371

Soft Charges and Electric-Magnetic Duality
text, January 2018

Hosseinzadeh, V.; Seraj, A.; Sheikh-Jabbari, M. M.
arXiv
DOI: 10.48550/arxiv.1806.01901

Asymptotic Charges and Coherent States in QCD
text, January 2019

Gonzo, Riccardo; McLoughlin, Tristan; Medrano, Diego
arXiv
DOI: 10.48550/arxiv.1906.11763

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

Kapec, Daniel; Mitra, Prahar
Journal of High Energy Physics, Vol. 2018, Issue 5
DOI: 10.1007/jhep05(2018)186

Uplifting AdS3/CFT2 to Flat Space Holography
text, January 2019

Ball, Adam; Himwich, Elizabeth; Narayanan, Sruthi A.
arXiv
DOI: 10.48550/arxiv.1905.09809

Uplifting AdS3/CFT2 to flat space holography
journal, August 2019

Ball, Adam; Himwich, Elizabeth; Narayanan, Sruthi A.
Journal of High Energy Physics, Vol. 2019, Issue 8
DOI: 10.1007/jhep08(2019)168

Celestial Amplitudes from UV to IR
text, January 2020

Arkani-Hamed, Nima; Pate, Monica; Raclariu, Ana-Maria
arXiv
DOI: 10.48550/arxiv.2012.04208

Electromagnetic duality and central charge
journal, December 2018

Freidel, Laurent; Pranzetti, Daniele
Physical Review D, Vol. 98, Issue 11
DOI: 10.1103/physrevd.98.116008

Soft charges and electric-magnetic duality
journal, August 2018

Hosseinzadeh, V.; Seraj, A.; Sheikh-Jabbari, M. M.
Journal of High Energy Physics, Vol. 2018, Issue 8
DOI: 10.1007/jhep08(2018)102

Conformally Soft Photons and Gravitons
text, January 2018

Donnay, Laura; Puhm, Andrea; Strominger, Andrew
arXiv
DOI: 10.48550/arxiv.1810.05219

Similar Records in DOE PAGES and OSTI.GOV collections:

4D scattering amplitudes and asymptotic symmetries from 2D CFT

Journal Article Cheung, Clifford ; de la Fuente, Anton ; Sundrum, Raman - Journal of High Energy Physics (Online)

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 correlatorsmore »« less
Cited by 130
https://doi.org/10.1007/JHEP01(2017)112

Full Text Available
$w_{1 + \infty}$ Algebra and the Celestial Sphere: Infinite Towers of Soft Graviton, Photon, and Gluon Symmetries

Journal Article Strominger, Andrew - Physical Review Letters

Imore »« less
https://doi.org/10.1103/PhysRevLett.127.221601
Celestial current algebra from Low’s subleading soft theorem

Journal Article Himwich, Elizabeth ; Strominger, Andrew - Physical Review. D.

The leading soft photon theorem implies that four-dimensional scattering amplitudes are controlled by a two-dimensional (2D) U(1) Kac-Moody symmetry that acts on the celestial sphere at null infinity (I). This celestial U(1) current is realized by components of the electromagnetic vector potential on the boundaries of I. Here, we develop a parallel story for Low's subleading soft photon theorem. It gives rise to a second celestial current, which is realized by vector potential components that are subleading in the large radius expansion about the boundaries of I. The subleading soft photon theorem is reexpressed as a celestial Ward identity formore »« less
Cited by 32
https://doi.org/10.1103/PhysRevD.100.065001
Kac-Moody algebras and string theory

Thesis/Dissertation Cleaver, Gerald B.

The focus of this thesis is on (1) the role of Kac-Moody algebras in string theory and the development of techniques for systematically building string theory models based on a higher level (K {>=} 2) KM algebras and (2) fractional superstrings, a new class of solutions based on SU(2){sub K}/U(1) conformal field theories. The content of this thesis is as follows. In chapter two they review KM algebras and their role in string theory. In the next chapter they present two results concerning the construction of modular invariant partition functions for conformal field theories build by tensoring together other conformalmore »« less
Full Text Available
Kac--Moody current algebras of D = 2 massless gauge theories, their representations and applications

Journal Article Craigie, N S ; Nahm, W ; Narain, K S - Ann. Phys. (N.Y.); (United States)

We give a classification of the Kac--Moody current algebras of all the possible massless fermion-gauge theories in two dimensions. It is shown that only Kac--Moody algebras based on A/sub N/, B/sub N/, C/sub N/, and D/sub N/ in the Cartan classification with all possible central charge occur.The representation of local fermion fields and simply laced Kac--Moody algebras with minimal central charge in terms of free boson fields on a compactified space is discussed in detail, where stress is laid on the role played by the boundary conditions on the various collective modes. Fractional solitons and the possible soliton representation ofmore »« less
https://doi.org/10.1016/0003-4916(87)90081-9

Similar Records

Title: Soft factorization in QED from 2D Kac-Moody symmetry

Abstract

Citation Formats

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

S-Duality and Helicity Amplitudes text, January 2015

Asymptotic symmetries of Yang-Mills theory journal, July 2014

A note on asymptotic symmetries and soft-photon theorem text, January 2014

Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere text, January 2017

4D scattering amplitudes and asymptotic symmetries from 2D CFT journal, January 2017

Asymptotic Symmetries of Yang-Mills Theory text, January 2013

Jet structure and infrared sensitive quantities in perturbative QCD journal, November 1983

Infrared divergences in QED revisited journal, October 2017

Magnetic Corrections to the Soft Photon Theorem text, January 2015

New symmetries of massless QED journal, October 2014

Projectors, Shadows, and Conformal Blocks text, January 2012

Remarks on Asymptotic Symmetries and the Sub-leading Soft Photon Theorem text, January 2016

Infrared divergences in QED revisited text, January 2017

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

Infrared Divergences in QED, Revisited text, January 2017

Null to time-like infinity Green's functions for asymptotic symmetries in Minkowski spacetime text, January 2015

Noether’s second theorem and Ward identities for gauge symmetries journal, February 2016

4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT text, January 2016

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

4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT text, January 2016

Magnetic Corrections to the Soft Photon Theorem journal, January 2016

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

Noether's Second Theorem and Ward Identities for Gauge Symmetries text, January 2015

Infrared Photons and Gravitons journal, October 1965

Flat space amplitudes and conformal symmetry of the celestial sphere journal, September 2017

Subleading soft photons and large gauge transformations journal, November 2016

Projectors, shadows, and conformal blocks journal, April 2014

Hard-soft-collinear factorization to all orders journal, November 2014

Scattering of Light of Very Low Frequency by Systems of Spin ½ journal, December 1954

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

Renormalization of the Wilson loops beyond the leading order journal, January 1987

A $d$-Dimensional Stress Tensor for Mink$_{d+2}$ Gravity text, January 2017

Soft Charges and Electric-Magnetic Duality text, January 2018

Asymptotic Charges and Coherent States in QCD text, January 2019

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

Uplifting AdS3/CFT2 to Flat Space Holography text, January 2019

Uplifting AdS3/CFT2 to flat space holography journal, August 2019

Celestial Amplitudes from UV to IR text, January 2020

Electromagnetic duality and central charge journal, December 2018

Soft charges and electric-magnetic duality journal, August 2018

Conformally Soft Photons and Gravitons text, January 2018

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

S-Duality and Helicity Amplitudes
text, January 2015

Asymptotic symmetries of Yang-Mills theory
journal, July 2014

A note on asymptotic symmetries and soft-photon theorem
text, January 2014

Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
text, January 2017

4D scattering amplitudes and asymptotic symmetries from 2D CFT
journal, January 2017

Asymptotic Symmetries of Yang-Mills Theory
text, January 2013

Jet structure and infrared sensitive quantities in perturbative QCD
journal, November 1983

Infrared divergences in QED revisited
journal, October 2017

Magnetic Corrections to the Soft Photon Theorem
text, January 2015

New symmetries of massless QED
journal, October 2014

Projectors, Shadows, and Conformal Blocks
text, January 2012

Remarks on Asymptotic Symmetries and the Sub-leading Soft Photon Theorem
text, January 2016

Infrared divergences in QED revisited
text, January 2017

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

Infrared Divergences in QED, Revisited
text, January 2017

Null to time-like infinity Green's functions for asymptotic symmetries in Minkowski spacetime
text, January 2015

Noether’s second theorem and Ward identities for gauge symmetries
journal, February 2016

4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
text, January 2016

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

4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
text, January 2016

Magnetic Corrections to the Soft Photon Theorem
journal, January 2016

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

Noether's Second Theorem and Ward Identities for Gauge Symmetries
text, January 2015

Infrared Photons and Gravitons
journal, October 1965

Flat space amplitudes and conformal symmetry of the celestial sphere
journal, September 2017

Subleading soft photons and large gauge transformations
journal, November 2016

Projectors, shadows, and conformal blocks
journal, April 2014

Hard-soft-collinear factorization to all orders
journal, November 2014

Scattering of Light of Very Low Frequency by Systems of Spin ½
journal, December 1954

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

Renormalization of the Wilson loops beyond the leading order
journal, January 1987

A $d$-Dimensional Stress Tensor for Mink$_{d+2}$ Gravity
text, January 2017

Soft Charges and Electric-Magnetic Duality
text, January 2018

Asymptotic Charges and Coherent States in QCD
text, January 2019

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

Uplifting AdS3/CFT2 to Flat Space Holography
text, January 2019

Uplifting AdS3/CFT2 to flat space holography
journal, August 2019

Celestial Amplitudes from UV to IR
text, January 2020

Electromagnetic duality and central charge
journal, December 2018

Soft charges and electric-magnetic duality
journal, August 2018

Conformally Soft Photons and Gravitons
text, January 2018