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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [INSPIRE].
J. Lee and R.M. Wald, Local symmetries and constraints, J. Math. Phys. 31 (1990) 725 [INSPIRE].
A. Ashtekar, L. Bombelli and O. Reula, The Covariant Phase Space Of Asymptotically Flat Gravitational Fields, PRINT-90-0318 (SYRACUSE) (1990), [INSPIRE].
A. Ashtekar, Asympotitc Quantization: Based on 1984 Naples Lectures, Monographs and Textbooks in physical science, 2, Bibliopolis, Naples, Italy, (1987).
M. Henneaux, Hamiltonian Form of the Path Integral for Theories with a Gauge Freedom, Phys. Rept. 126 (1985) 1 [INSPIRE].
M. Henneaux and C. Teitelboim, Quantization of gauge systems, Princeton University Press, Princeton, U.S.A., (1992).
J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].
M. Henneaux and C. Troessaert, Asymptotic symmetries of electromagnetism at spatial infinity, JHEP 05 (2018) 137 [arXiv:1803.10194] [INSPIRE].
M. Henneaux and C. Troessaert, Hamiltonian structure and asymptotic symmetries of the Einstein-Maxwell system at spatial infinity, JHEP 07 (2018) 171 [arXiv:1805.11288] [INSPIRE].
D. Kapec, M. Pate and A. Strominger, New Symmetries of QED, Adv. Theor. Math. Phys. 21 (2017) 1769 [arXiv:1506.02906] [INSPIRE].
L. Bieri, P. Chen and S.-T. Yau, The Electromagnetic Christodoulou Memory Effect and its Application to Neutron Star Binary Mergers, Class. Quant. Grav. 29 (2012) 215003 [arXiv:1110.0410] [INSPIRE].
L. Bieri and D. Garfinkle, An electromagnetic analogue of gravitational wave memory, Class. Quant. Grav. 30 (2013) 195009 [arXiv:1307.5098] [INSPIRE].
L. Susskind, Electromagnetic Memory, arXiv:1507.02584 [INSPIRE].
S. Pasterski, Asymptotic Symmetries and Electromagnetic Memory, JHEP 09 (2017) 154 [arXiv:1505.00716] [INSPIRE].
Y. Hamada, M.-S. Seo and G. Shiu, Large gauge transformations and little group for soft photons, Phys. Rev. D 96 (2017) 105013 [arXiv:1704.08773] [INSPIRE].
Y. Hamada and G. Shiu, Infinite Set of Soft Theorems in Gauge-Gravity Theories as Ward-Takahashi Identities, Phys. Rev. Lett. 120 (2018) 201601 [arXiv:1801.05528] [INSPIRE].
H. Hirai and S. Sugishita, Conservation Laws from Asymptotic Symmetry and Subleading Charges in QED, JHEP 07 (2018) 122 [arXiv:1805.05651] [INSPIRE].
E.E. Flanagan and D.A. Nichols, Observer dependence of angular momentum in general relativity and its relationship to the gravitational-wave memory effect, Phys. Rev. D 92 (2015) 084057 [arXiv:1411.4599] [INSPIRE].
L. Bieri, D. Garfinkle and S.-T. Yau, Gravitational Waves and Their Memory in General Relativity, arXiv:1505.05213 [INSPIRE].
A. Tolish, L. Bieri, D. Garfinkle and R.M. Wald, Examination of a simple example of gravitational wave memory, Phys. Rev. D 90 (2014) 044060 [arXiv:1405.6396] [INSPIRE].
M. Pate, A.-M. Raclariu and A. Strominger, Gravitational Memory in Higher Dimensions, JHEP 06 (2018) 138 [arXiv:1712.01204] [INSPIRE].
S.B. Giddings and A. Kinsella, Gauge-invariant observables, gravitational dressings and holography in AdS, arXiv:1802.01602 [INSPIRE].
P.P. Kulish and L.D. Faddeev, Asymptotic conditions and infrared divergences in quantum electrodynamics, Theor. Math. Phys. 4 (1970) 745 [INSPIRE].
B. Gabai and A. Sever, Large gauge symmetries and asymptotic states in QED, JHEP 12 (2016) 095 [arXiv:1607.08599] [INSPIRE].
A. Herdegen, Asymptotic structure of electrodynamics revisited, Lett. Math. Phys. 107 (2017) 1439 [arXiv:1604.04170] [INSPIRE].
C. Montonen and D.I. Olive, Magnetic Monopoles as Gauge Particles?, Phys. Lett. B 72 (1977) 117 [INSPIRE].
N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [Erratum ibid. B 430 (1994) 485] [hep-th/9407087] [INSPIRE].
A. Strominger, Magnetic Corrections to the Soft Photon Theorem, Phys. Rev. Lett. 116 (2016) 031602 [arXiv:1509.00543] [INSPIRE].
M. Campiglia and A. Laddha, Subleading soft photons and large gauge transformations, JHEP 11 (2016) 012 [arXiv:1605.09677] [INSPIRE].
D. Zwanziger, Quantum field theory of particles with both electric and magnetic charges, Phys. Rev. 176 (1968) 1489 [INSPIRE].
D. Zwanziger, Local Lagrangian quantum field theory of electric and magnetic charges, Phys. Rev. D 3 (1971) 880 [INSPIRE].
C. Cardona, Asymptotic Symmetries of Yang-Mills with Theta Term and Monopoles, arXiv:1504.05542 [INSPIRE].
L. Freidel and D. Pranzetti, Electromagnetic duality and central charge, arXiv:1806.03161 [INSPIRE].
A. Seraj, Conserved charges, surface degrees of freedom and black hole entropy, Ph.D. thesis, IPM, Tehran, 2016. arXiv:1603.02442 [INSPIRE].
A. Fiorucci and G. Compère, Advanced Lectures in General Relativity, Ph.D. thesis, Brussels U., PTM, 2018. arXiv:1801.07064 [INSPIRE].
N. Woodhouse, Geometric Quantization, Oxford Mathematical Monographs, Clarendon, Oxford, U.K. (1980).
J.D. Jackson, Classical Electrodynamics, Wiley, (1998).
A. Seraj, Multipole charge conservation and implications on electromagnetic radiation, JHEP 06 (2017) 080 [arXiv:1610.02870] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries of QED and Weinberg’s soft photon theorem, JHEP 07 (2015) 115 [arXiv:1505.05346] [INSPIRE].
W. Donnelly and L. Freidel, Local subsystems in gauge theory and gravity, JHEP 09 (2016) 102 [arXiv:1601.04744] [INSPIRE].
M. Geiller, Edge modes and corner ambiguities in 3d Chern-Simons theory and gravity, Nucl. Phys. B 924 (2017) 312 [arXiv:1703.04748] [INSPIRE].
M. Geiller, Lorentz-diffeomorphism edge modes in 3d gravity, JHEP 02 (2018) 029 [arXiv:1712.05269] [INSPIRE].
A.J. Speranza, Local phase space and edge modes for diffeomorphism-invariant theories, JHEP 02 (2018) 021 [arXiv:1706.05061] [INSPIRE].
T. He, P. Mitra, A.P. Porfyriadis and A. Strominger, New Symmetries of Massless QED, JHEP 10 (2014) 112 [arXiv:1407.3789] [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038] [INSPIRE].
V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
K.Y. Bliokh, A.Y. Bekshaev and F. Nori, Dual electromagnetism: Helicity, spin, momentum and angular momentum, New J. Phys. 15 (2013) 033026 [arXiv:1208.4523] [INSPIRE].
R.P. Cameron and S.M. Barnett, Electric-magnetic symmetry and Noether’s theorem, New J. Phys. 14 (2012) 123019.
S. Deser and C. Teitelboim, Duality Transformations of Abelian and Nonabelian Gauge Fields, Phys. Rev. D 13 (1976) 1592 [INSPIRE].
G. Barnich and A. Gomberoff, Dyons with potentials: Duality and black hole thermodynamics, Phys. Rev. D 78 (2008) 025025 [arXiv:0705.0632] [INSPIRE].
C. Bunster, A. Gomberoff and A. Pérez, Regge-Teitelboim analysis of the symmetries of electromagnetic and gravitational fields on asymptotically null spacelike surfaces, arXiv:1805.03728 [INSPIRE].
T. Regge and C. Teitelboim, Role of Surface Integrals in the Hamiltonian Formulation of General Relativity, Annals Phys. 88 (1974) 286 [INSPIRE].
A. Bhattacharyya, L.-Y. Hung and Y. Jiang, Null hypersurface quantization, electromagnetic duality and asymptotic symmetries of Maxwell theory, JHEP 03 (2018) 027 [arXiv:1708.05606] [INSPIRE].
Y. Hamada, M.-S. Seo and G. Shiu, Electromagnetic Duality and the Electric Memory Effect, JHEP 02 (2018) 046 [arXiv:1711.09968] [INSPIRE].
R.P. Cameron, S.M. Barnett and A.M. Yao, Optical helicity, optical spin and related quantities in electromagnetic theory, New J. Phys. 14 (2012) 053050.
S. Weinberg, Photons and Gravitons in s Matrix Theory: Derivation of Charge Conservation and Equality of Gravitational and Inertial Mass, Phys. Rev. 135 (1964) B1049 [INSPIRE].
G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062 [arXiv:1001.1541] [INSPIRE].
G. Barnich and C. Troessaert, BMS charge algebra, JHEP 12 (2011) 105 [arXiv:1106.0213] [INSPIRE].
G. Barnich, Centrally extended BMS 4 Lie algebroid, JHEP 06 (2017) 007 [arXiv:1703.08704] [INSPIRE].
E. Bogomolny, S. Mashkevich and S. Ouvry, Scattering on two Aharonov-Bohm vortices with opposite fluxes, J. Phys. A 43 (2010) 354029 [arXiv:1003.0294] [INSPIRE].
C. Cheung, A. de la Fuente and R. Sundrum, 4D scattering amplitudes and asymptotic symmetries from 2D CFT, JHEP 01 (2017) 112 [arXiv:1609.00732] [INSPIRE].
A. Nande, M. Pate and A. Strominger, Soft Factorization in QED from 2D Kac-Moody Symmetry, JHEP 02 (2018) 079 [arXiv:1705.00608] [INSPIRE].
H. Afshar, D. Grumiller, W. Merbis, A. Pérez, D. Tempo and R. Troncoso, Soft hairy horizons in three spacetime dimensions, Phys. Rev. D 95 (2017) 106005 [arXiv:1611.09783] [INSPIRE].
H. Afshar, D. Grumiller and M.M. Sheikh-Jabbari, Near horizon soft hair as microstates of three dimensional black holes, Phys. Rev. D 96 (2017) 084032 [arXiv:1607.00009] [INSPIRE].
H. Afshar, D. Grumiller, M.M. Sheikh-Jabbari and H. Yavartanoo, Horizon fluff, semi-classical black hole microstates — Log-corrections to BTZ entropy and black hole/particle correspondence, JHEP 08 (2017) 087 [arXiv:1705.06257] [INSPIRE].
H. Afshar, E. Esmaeili and M.M. Sheikh-Jabbari, Asymptotic Symmetries in p-Form Theories, JHEP 05 (2018) 042 [arXiv:1801.07752] [INSPIRE].
C. Bunster and M. Henneaux, Can (Electric-Magnetic) Duality Be Gauged?, Phys. Rev. D 83 (2011) 045031 [arXiv:1011.5889] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1806.01901
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Hosseinzadeh, V., Seraj, A. & Sheikh-Jabbari, M.M. Soft charges and electric-magnetic duality. J. High Energ. Phys. 2018, 102 (2018). https://doi.org/10.1007/JHEP08(2018)102
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2018)102