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 ± of (d + 2)-dimensional Minkowski spacetime. These symmetries are parameterized by an arbitrary function ε(x) of the d-dimensional celestial sphere living at ±. 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.
Highlights
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
Of all the soft theorems is that the soft factor is universal, i.e. it does not depend on the details of the theory under consideration
Such universality naturally suggests that perhaps the soft theorems arise from some underlying symmetry, and it was relatively recently discovered that these theorems are precisely the Ward identities associated to the asymptotic symmetries of scattering amplitudes
Summary
Lowercase Latin indices are raised and lowered by the Kronecker delta δab and δab, respectively. Using these coordinates, the metric of Minkowski spacetime becomes ds2 = ηABdXAdXB = −dudr + r2δabdxadxb,. The null boundaries I ± are located at r → ±∞ while keeping (u, xa) fixed. On this hypersurface, xa is the stereographic coordinate on the celestial sphere. A U(1) gauge theory is described by a field strength Fμν and matter fields Ψi. Dynamics of the field strength is described by Maxwell’s equations and the Bianchi identity, given respectively by e2Jν = ∇μFμν 0 = ∂αFμν + ∂ν Fαμ + ∂μFνα. Gauge transformations that vanish at infinity correspond to redundant descriptions of the same physical state and can be eliminated by a choice of gauge
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