Generalized asymptotics for gauge fields

Abstract

An interesting question is to characterize the general class of allowed boundary conditions for gauge theories, including gravity, at spatial and null infinity. This has played a role in discussions of soft charges, where antipodal symmetry has typically been assumed. However, the existence of electric and gravitational line operators, arising from gauge-invariant dressed observables, for example associated to axial or Fefferman-Graham like gauges, indicates the existence of non-antipodally symmetric initial data. This note studies aspects of the solutions corresponding to such non-symmetric initial data. The explicit evolution can be found, via a Green function, and bounds can be given on the asymptotic behavior of such solutions, evading arguments for singular behavior. Likewise, objections to such solutions based on infinite symplectic form are also avoided, although these solutions may be superselected. Soft charge conservation laws, and their modification, are briefly examined for such solutions. This discussion strengthens (though is not necessary for) arguments that soft charges characterize gauge field degrees of freedom, but not necessarily the degrees of freedom associated to the matter sourcing the field.

Gauge-invariant observables in gravity and electromagnetism: Black hole backgrounds and null dressings

“…The difference between two distinct such field configurations, satisfying (9), is a pure radiation (sourceless) field. So, for example, the gravitational line dressing (8), which may also be put in this form, creates a field configuration that, in the case of a fixed static source, is expected to emit radiation to infinity and asymptote to the symmetrical Coulomb-like solution in the future [8], in parallel with the decay of the analogous electromagnetic Faraday line [25][26][27][28]. Thus, in general, different dressings correspond to different radiation fields superposed on a given dressing, and for example have different soft charges [10].…”

“…This is also of the general form (31), with anĚ i corresponding to a Coulomb field. The corresponding 6 For previous discussions of EM dressings, see [31][32][33][34] and [28]. 7 A related construction given by Mandelstam [35] is to run such a line back in time to a fiducial time, and then to infinity in the corresponding spatial slice, rather than running the line to infinity at equal time to the original operator.…”

A note on electric-magnetic duality and soft charges

“…Both electric and magnetic dressings are necessary in the presence of magnetic poles [31]. Most dressings are JHEP06(2020)081 usually chosen not to fulfill any particular parity conditions [32,33], leading to divergences in the boost generators, which must be regulated. Given the ambiguity in the dressing of physical states, one might consider dressings that fulfill our (twisted) parity conditions.…”

Source and response soft charges for Maxwell theory on AdSd

“…We also discuss how the AdS d isometry charges act on our soft mode phase space. In section 7, we show how our results on AdS d and those studied in the literature for Maxwell theory on flat space [19][20][21][22][23][24][25][26][27] could be related to each other through an AdS (large radius) flat space limit. In particular, we show that only the source boundary gauge transformations and the associated soft charges survive the limit and the response charges become subdominant and do not appear in the limit.…”