Low’s Subleading Soft Theorem as a Symmetry of QED

Abstract

It was shown by Low in the 1950s that the subleading terms of soft-photon S-matrix elements obey a universal linear relation. In this Letter, we give a new interpretation to this old relation, for the case of massless QED, as an infinitesimal symmetry of the S matrix. The symmetry is shown to be locally generated by a vector field on the conformal sphere at null infinity. Explicit expressions are constructed for the associated charges as integrals over null infinity and shown to generate the symmetry. These charges are local generalizations of electric and magnetic dipole charges.

The double copy structure of soft gravitons

“…This is an added complication when investigating higher-point amplitudes. Another interesting problem to address is the implications of our results for the possible relation between the asymptotic symmetries of gauge theories [15,30] and gravity [5,6]. These and other issues will be studied elsewhere.…”

“…In QED, the subleading corrections also admit an interpretation in terms of the asymptotic symmetries of the theory at null infinity [15]. Low's theorem was originally derived in the limit in which the momentum of the photon is taken to be very small, k → 0.…”

Subleading soft photons and large gauge transformations

“…While S (1) is expected to be sensitive to loop corrections [6,7] our focus will be on the theorem at tree level. A natural question, first investigated by Lysov, Pasterski and Strominger [11] is whether Low's theorem can also be understood as Ward identities. In [11] the authors showed that the theorem is equivalent to Ward identities of infinitely many charges that are parametrized by vector fields on the sphere.…”

“…As shown by Low [10] the factorization of scattering amplitudes applies also to the next order in the photon energy. The theorem takes the form [11]:…”

Asymptotic symmetries, holography and topological hair

“…Considerable progress has been made in this regard by the discovery that the associated large diffeomorphisms and gauge transformations arise as soft limits of physical gravitational and gauge fields emerging from scattering processes [5][6][7][8][9][10][11][12][13][14][15], as captured by the Weinberg Soft Theorems [16][17][18][19][20]. The infinite-dimensional AS then describe the soft field dressing of a hard process, and are sensitive to the passage of charge/energy-momentum as a function of angle, through "memory" effects [21][22][23][24][25][26][27][28][29][30].…”