Soft charges and electric-magnetic duality

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.

Scalar asymptotic charges and dual large gauge transformations

“…The existence of the auxiliary two-form theory should also give us confidence that the commutation relations we find are consistent, since they follow from obvious transformation rules in the two-form theory. This perspective is similar to recent understanding [18,19] of the two polarisations of soft photons in QED in terms of electric and magnetic large gauge transformations.…”

“…The full gaugetransformation operator on a lattice without a boundary, which we include for completeness, is On a lattice with a boundary, however, we have to distinguish between large and small gauge transformations. 18 Small gauge transformations are generated by operators of the form (5.5) on interior links, which are links for which all four adjoining faces are actually in the lattice. Large gauge transformations are generated by operators similar to (5.5) on boundary links, except that we remove the Es that live on non-existent faces.…”

Electromagnetic and color memory in even dimensions

“…The very existence of the latter, on the other hand, was sometimes doubted in the literature because of the need for too-slow falloffs on the gauge potentials that could in principle lead to divergences in physically sensible quantities. 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].…”

Asymptotic symmetries of Maxwell theory in arbitrary dimensions at spatial infinity

“…For the separately-treated 3d theory, a set of non-logarithmic boundary conditions at null infinity are derived by large boost limit.Recent interest in ASG of Maxwell theory in flat space emanated from the discovery that soft photon theorem in QED is the Ward identity of the asymptotic symmetry group [7,8]. Concerned with that motivation, research on asymptotic symmetries is mostly performed in null slicing (Bondi coordinates) of flat space, where the surface of integration is (almost) lightlike-separated from the scattering event [7,[9][10][11][12][13][14]. The charges "at null infinity" have also been generalized to subleading orders [15][16][17].The asymptotic symmetry group of Maxwell theory at spatial infinity is, as far as we know, restricted to three and four dimensions [15,[18][19][20][21].…”

“…Parity of π B can not be inferred from leading fields. For electric dipoles, π B (−x) = +π B (x) 13. It exists also in higher dimensions.…”