Abstract
We study the effect of electromagnetic interactions on the classical soft theorems on an asymptotically AdS background in 4 spacetime dimensions, in the limit of a small cosmological constant or equivalently a large AdS radius l. This identifies 1/l2 perturbative corrections to the known asymptotically flat spacetime leading and subleading soft factors. Our analysis is only valid to leading order in 1/l2. The leading soft factor can be expected to be universal and holds beyond tree level. This allows us to derive a 1/l2 corrected Ward identity, following the known equivalence between large gauge Ward identities and soft theorems in asymptotically flat spacetimes.
Highlights
Of the single soft photon theorem to subleading order in four spacetime dimensions [20]: Seflmat = Seflmat;leading + Seflmat;subleading, with
We study the effect of electromagnetic interactions on the classical soft theorems on an asymptotically Anti-de Sitter (AdS) background in 4 spacetime dimensions, in the limit of a small cosmological constant or equivalently a large AdS radius l
We find the effect of the small AdS potential on the classical soft photon theorem
Summary
We are interested in studying the classical soft photon theorem in asymptotically AdS backgrounds. Since we are interested in studying the radiation emitted by the scattering of a probe particle moving in an unbounded trajectory on the spacetime (from the point of view of an asymptotic observer) we introduce isotropic coordinates. We refer the reader to [33] for further justification on choosing this particular coordinate system In these coordinates, the resulting radiation will be isotropic in all spatial directions. Retaining terms up to leading order in φ and 1/l2, we find that the metric components in (2.8) take the form ρ2 g00 = − 1 + 2φ + l2 , g0i = 0 , ρ2 gij = δij 1 − 2φ + 2l2. Note that the spacetime metric in (2.12) provides the leading AdS correction about an asymptotically flat spacetime and in isotropic coordinates it just behaves like the AdSSchwarzschild metric with a gauge potential. √ 3The equality of GQ and GM holds in the extremal limit
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