Soft charges and electric-magnetic duality

Journal of High Energy Physics, Aug 2018

Abstract The main focus of this work is to study magnetic soft charges of the four dimensional Maxwell theory. Imposing appropriate asymptotic falloff conditions, we compute the electric and magnetic soft charges and their algebra both at spatial and at null infinity. While the commutator of two electric or two magnetic soft charges vanish, the electric and magnetic soft charges satisfy a complex U(1) current algebra. This current algebra through Sugawara construction yields two U(1) Kac-Moody algebras. We repeat the charge analysis in the electric-magnetic duality-symmetric Maxwell theory and construct the duality-symmetric phase space where the electric and magnetic soft charges generate the respective boundary gauge transformations. We show that the generator of the electric-magnetic duality and the electric and magnetic soft charges form infinite copies of iso(2) algebra. Moreover, we study the algebra of charges associated with the global Poincaré symmetry of the background Minkowski spacetime and the soft charges. We discuss physical meaning and implication of our charges and their algebra.

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Soft charges and electric-magnetic duality

Journal of High Energy Physics August 2018, 2018:102 | Cite as Soft charges and electric-magnetic duality AuthorsAuthors and affiliations V. HosseinzadehA. SerajM. M. Sheikh-Jabbari Open Access Regular Article - Theoretical Physics First Online: 17 August 2018 Received: 07 July 2018 Accepted: 07 August 2018 45 Downloads Abstract The main focus of this work is to study magnetic soft charges of the four dimensional Maxwell theory. Imposing appropriate asymptotic falloff conditions, we compute the electric and magnetic soft charges and their algebra both at spatial and at null infinity. While the commutator of two electric or two magnetic soft charges vanish, the electric and magnetic soft charges satisfy a complex U(1) current algebra. This current algebra through Sugawara construction yields two U(1) Kac-Moody algebras. We repeat the charge analysis in the electric-magnetic duality-symmetric Maxwell theory and construct the duality-symmetric phase space where the electric and magnetic soft charges generate the respective boundary gauge transformations. We show that the generator of the electric-magnetic duality and the electric and magnetic soft charges form infinite copies of iso(2) algebra. Moreover, we study the algebra of charges associated with the global Poincaré symmetry of the background Minkowski spacetime and the soft charges. We discuss physical meaning and implication of our charges and their algebra. Keywords Duality in Gauge Field Theories Gauge Symmetry Global Symmetries Spontaneous Symmetry Breaking  ArXiv ePrint: 1806.01901 Download to read the full article text Notes Open Access This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. References [1] A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [INSPIRE]. [2] J. Lee and R.M. Wald, Local symmetries and constraints, J. Math. Phys. 31 (1990) 725 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [3] A. Ashtekar, L. Bombelli and O. Reula, The Covariant Phase Space Of Asymptotically Flat Gravitational Fields, PRINT-90-0318 (SYRACUSE) (1990), [INSPIRE]. [4] A. 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V. Hosseinzadeh, A. Seraj, M. M. Sheikh-Jabbari. Soft charges and electric-magnetic duality, Journal of High Energy Physics, 2018, 102, DOI: 10.1007/JHEP08(2018)102