Abstract
It is now well understood that Ward identities associated to the (extended) BMS algebra are equivalent to single soft graviton theorems. In this work, we show that if we consider nested Ward identities constructed out of two BMS charges, a class of double soft factorization theorems can be recovered. By making connections with earlier works in the literature, we argue that at the sub-leading order, these double soft graviton theorems are the so-called consecutive double soft graviton theorems. We also show how these nested Ward identities can be understood as Ward identities associated to BMS symmetries in scattering states defined around (non-Fock) vacua parametrized by supertranslations or superrotations.
Highlights
The leading single soft graviton theorem follows from the Ward identity of the supertranslation charge Qf [1], which physically corresponds to the conservation of energy at each direction on the conformal sphere at null infinity
Having reviewed the relationship between Ward identities associated to the asymptotic symmetries and single soft graviton theorems, we ask if there are Ward identities in the theory which are equivalent to the double soft graviton theorems at the leading and sub–leading order
If we consider Ward identities associated to superrotation charges QV in this supertranslated vacuum, we are led to one of the two consecutive subleading double soft graviton theorems
Summary
We begin by reviewing the derivations of the single soft graviton theorems (both leading and sub–leading) from asymptotic symmetries [1, 12]. The asymptotic symmetry group of gravity, acting on the asymptotic phase space of gravity is the “Generalised BMS” group — it is a semidirect product of supertranslations and Diff(S2). They can be thought of as a local generalization of translations and the Lorentz group respectively. To define a symmetry of a gravitational scattering problem at the quantum level, these charges are elevated to a symmetry of the quantum gravity S–matrix. Corresponding to each such symmetry one gets a Ward identity. We discuss that how the single soft graviton theorems are equivalent to Ward identities of generalised BMS charges
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