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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:
 [1]; ORCiD logo [1];  [1]
  1. Harvard Univ., Cambridge, MA (United States). Dept. of Physics
Publication Date:
Research Org.:
Harvard Univ., Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1505226
Grant/Contract Number:  
SC0007870
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
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.
Nande, Anjalika, Pate, Monica, & Strominger, Andrew. Soft factorization in QED from 2D Kac-Moody symmetry. United States. doi:10.1007/jhep02(2018)079.
Nande, Anjalika, Pate, Monica, and Strominger, Andrew. Wed . "Soft factorization in QED from 2D Kac-Moody symmetry". United States. doi:10.1007/jhep02(2018)079. https://www.osti.gov/servlets/purl/1505226.
@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)},
issn = {1029-8479},
number = 2,
volume = 2018,
place = {United States},
year = {2018},
month = {2}
}

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Cited by: 9 works
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Works referenced in this record:

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

Infrared Photons and Gravitons
journal, October 1965


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


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

Remarks on asymptotic symmetries and the subleading soft photon theorem
journal, January 2017


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

Asymptotic symmetries of Yang-Mills theory
journal, July 2014


Jet physics from static charges in AdS space
journal, February 2012

  • Chien, Yang-Ting; Schwartz, Matthew D.; Simmons-Duffin, David
  • Physical Review D, Vol. 85, Issue 4
  • DOI: 10.1103/PhysRevD.85.045010

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


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


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


Magnetic Corrections to the Soft Photon Theorem
journal, January 2016


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


Null to time-like infinity Green’s functions for asymptotic symmetries in Minkowski spacetime
journal, November 2015


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

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


Deep inelastic scattering as x 1 using soft-collinear effective theory
journal, December 2003


Infrared divergences in QED revisited
journal, October 2017


A note on asymptotic symmetries and soft-photon theorem
journal, February 2015


S-duality and helicity amplitudes
journal, March 2016