Asymptotic symmetries and Weinberg’s soft photon theorem in Minkd+2

Abstract

We show that Weinberg's leading soft photon theorem in massless abelian gauge theories implies the existence of an infinite-dimensional large gauge symmetry which acts non-trivially on the null boundaries I ± of (d + 2)-dimensional Minkowski spacetime. These symmetries are parameterized by an arbitrary function ε(x) of the d-dimensional celestial sphere living at I ± . This extends the previously established equivalence between Weinberg's leading soft theorem and asymptotic symmetries from four and higher even dimensions to all higher dimensions.The remaining ones are then determined by Lorentz invariance. Similarly, the fall-offs for the Coulombic part are determined by Gauss's law, which also determines the fall-offs for the matter current(2.10)We would now like to determine the precise large r expansion for both the radiative and the Coulombic fields.4 As we shall see in (2.23), in odd dimensions, the radiative field has an expansion in both integer and half-integer powers of |r|, as indicated in the first column of (2.9). In even dimensions, we obtain later in (2.27) that the radiative field has an expansion in integer powers of |r|, though non-analytic terms of the form log r are also present (not shown in (2.9)).

Electromagnetic and color memory in even dimensions

“…We would like to show that the surface charges defined in Section 5.2 enter Weinberg's soft theorem [48,49]. More precisely, we will see how the Weinberg theorem implies the validity of the Ward identities associated to such charges in D ≥ 4 [33,34].…”

“…In order to retrieve it, one needs a more general ansatz. We find that it is sufficient, to this purpose, to consider the following type of asymptotic expansion 9 involving also a logarithmic dependence on r [29,[33][34][35]:…”

“…Similar arguments showing the finiteness of the Hamiltonian charge in higherdimensions have been given, in the case of linearised spin-two case in retarded Bondi gauge, in [44], while a renormalisation procedure has been recently proposed, for the Maxwell theory in the radial gauge, in [45] (for the general definition of surface charges see [46]). The relation between asymptotic charges and the soft photon theorem in any D was recently clarified in [33,34]. In Appendix D we present the details of the computation for the case of interest in our work.…”

“…The asymptotic structure of spin-one gauge theories, in particular in connection to soft theorems was widely investigated in the literature [19][20][21][22][23][24][25][26][27][28][29][30][31][32]. More recently, the issue concerning the higher-dimensional extensions of those results was further explored in a number of works [33][34][35][36]. On our side, in Section 5 we provide an analysis of the asymptotic symmetries of Maxwell's theory in any D, even and odd, stressing analogies and differences between the two cases, always working in the Lorenz gauge.…”

Asymptotic renormalization in flat space: symplectic potential and charges of electromagnetism

“…Such charges corresponds to divergent transformation of the field in the absence of renormalization [50]. Also, it is clear that our analysis can be extended to include the analysis of the odd-dimensional case (see [53] for a recent discussion about odd dimension).…”