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We show that large gauge transformations in asymptotically flat spacetime can be implemented by sandwiching a shell containing the ingoing hard particles between two finite-width shells of soft gauge excitations. Integration of the graviton Dirac bracket implies that our observable soft degrees of freedom obey the algebra imposed by Strominger on unobservable boundary degrees of freedom. Thus, we provide both a derivation and an observable realization of this algebra. The conservation laws associated with asymptotic symmetries are seen to arise physically from free propagation of infrared modes. This explains in physical terms our recent result that soft charges fail to constrain the hard scattering problem, and so cannot be relevant to the black hole information paradox.
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In this paper, we revisit the question of identifying Soft Graviton theorem in higher (even) dimensions with Ward identities associated with Asymptotic symmetries. Building on the prior work of cite{strominger}, we compute, from first principles, the (asymptotic) charge associated to Supertranslation symmetry in higher even dimensions and show that (i) these charges are non-trivial, finite and (ii) the corresponding Ward identities are indeed the soft graviton theorems.
Recently it was conjectured that a certain infinite-dimensional diagonal subgroup of BMS supertranslations acting on past and future null infinity (${mathscr I}^-$ and ${mathscr I}^+$) is an exact symmetry of the quantum gravity ${cal S}$-matrix, and an associated Ward identity was derived. In this paper we show that this supertranslation Ward identity is precisely equivalent to Weinbergs soft graviton theorem. Along the way we construct the canonical generators of supertranslations at ${mathscr I}^pm$, including the relevant soft graviton contributions. Boundary conditions at the past and future of ${mathscr I}^pm$ and a correspondingly modified Dirac bracket are required. The soft gravitons enter as boundary modes and are manifestly the Goldstone bosons of spontaneously broken supertranslation invariance.
The area of a cross-sectional cut $Sigma$ of future null infinity ($mathcal{I}^+$) is infinite. We define a finite, renormalized area by subtracting the area of the same cut in any one of the infinite number of BMS-degenerate classical vacua. The renormalized area acquires an anomalous dependence on the choice of vacuum. We relate it to the modular energy, including a soft graviton contribution, of the region of $mathcal{I}^+$ to the future of $Sigma$. Under supertranslations, the renormalized area shifts by the supertranslation charge of $Sigma$. In quantum gravity, we conjecture a bound relating the renormalized area to the entanglement entropy across $Sigma$ of the outgoing quantum state on $mathcal{I}^+$.
Recently it has been shown that infrared divergences in the conventional S-matrix elements of gauge and gravitational theories arise from a violation of the conservation laws associated with large gauge symmetries. These infrared divergences can be cured by using the Faddeev-Kulish (FK) asymptotic states as the basis for S-matrix elements. Motivated by this connection, we study the action of BMS supertranslations on the FK asymptotic states of perturbative quantum gravity. We compute the BMS charge of the FK states and show that it characterizes the superselection sector to which the state belongs. Conservation of the BMS charge then implies that there is no transition between different superselection sectors, hence showing that the FK graviton clouds implement the necessary vacuum transition induced by the scattering process.
We construct the Faddeev-Kulish asymptotic states in a quantum field theory of electric and magnetic charges. We find that there are two kind of dressings: apart from the well known (electric) Wilson line dressing, there is a magnetic counterpart which can be written as a t Hooft line operator. The t Hooft line dressings are charged under the magnetic large gauge transformation (LGT), but are neutral under electric LGT. This is in contrast to the Faddeev-Kulish dressings of electrons, which can be written as a Wilson line operator and are charged under electric LGT but neutral under magnetic LGT. With these dressings and the corresponding construction of the coherent states, the infrared finiteness of the theory of electric and magnetic charges is guaranteed. Even in the absence of magnetic monopoles, the electric and magnetic soft modes exhibit the electromagnetic duality of vacuum Maxwell theory. Using only the asymptotic form of three-point interactions in a field theory of electric and magnetic charges, we show that the leading magnetic dressings, like the leading electric ones, are exact in the field theory of electric and magnetic charges, in accordance with a conjecture of Strominger. We then extend the construction to perturbative quantum gravity in asymptotically flat spacetime, and construct gravitational t Hooft line dressings that are charged under dual supertranslations. The duality in the quantum theory between the electric and magnetic soft charges and their dressings is thus made manifest.
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