Advances in Theoretical and Mathematical Physics

Volume 21 (2017)

Number 7

Special Issue: Proceedings of the Strings 2016 Conference in Beijing

Guest Editors: J. Maldacena (Institute for Advanced Study), H. Ooguri (California Institute of Technology), H. Babak (Harvard University), S. Li (Tsinghua University), W. Song (Tsinghua University), and H. Lin (Tsinghua University)

Asymptotic symmetries of massless QED in even dimensions

Pages: 1747 – 1767



Daniel Kapec (Center for the Fundamental Laws of Nature, Harvard University, Cambridge, Massacusetts, U.S.A.)

Vyacheslav Lysov (Institute for Theoretical Physics, California Institute of Technology, Pasadena, Cal., U.S.A.)

Andrew Strominger (Center for the Fundamental Laws of Nature, Harvard University, Cambridge, Massacusetts, U.S.A.)


We consider the scattering of massless particles coupled to an abelian gauge field in $2n$-dimensional Minkowski spacetime. Weinberg’s soft photon theorem is recast asWard identities for infinitely many new nontrivial symmetries of the massless QED $\mathcal{S}$-matrix, with one such identity arising for each propagation direction of the soft photon. These symmetries are identified as large gauge transformations with angle-dependent gauge parameters that are constant along the null generators of null infinity. Almost all of the symmetries are spontaneously broken in the standard vacuum and the soft photons are the corresponding Goldstone bosons. Our result establishes a relationship between soft theorems and asymptotic symmetry groups in any even dimension.

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We are grateful to T. He, D. Jafferis, P. Mitra, S. Pasterski, A. Porfyriadis, M. Schwartz and A. Zhiboedov for useful conversations. This work was supported in part by DOE grant DE-FG02-91ER40654 and the Fundamental Laws Initiative at Harvard. The work of V.L. is supported in part by the Sherman Fairchild scholarship and DOE grant DE-SC0011632.

Published 19 March 2018