On BMS invariance of gravitational scattering

By Andrew Strominger. 2013

877 citations recorded by the source corpus.

A bstractBMS+ transformations act nontrivially on outgoing gravitational scattering data while preserving intrinsic structure at future null infinity (ℐ$$ \mathrm{\mathcal{I}} $$+). BMS− transformations similarly act on ingoing data at past null infinity (ℐ$$ \mathrm{\mathcal{I}} $$−). In this paper we apply — within a suitable finite neighborhood of the Minkowski vacuum — results of Christodoulou and Klainerman to link ℐ$$ \mathrm{\mathcal{I}} $$+ to ℐ$$ \mathrm{\mathcal{I}} $$− and thereby identify “diagonal” elements BMS0 of BMS+ × BMS−. We argue that BMS0 is a nontrivial infinite-dimensional symmetry of both classical gravitational scattering and the quantum gravity S$$ \mathcal{S} $$-matrix. It implies the conservation of net accumulated energy flux at every angle on the conformal S2 at ℐ$$ \mathrm{\mathcal{I}} $$. The associated Ward identity is shown to relate S-matrix elements with and without soft gravitons. Finally, BMS0 is recast as a U(1) Kac-Moody symmetry and an expression for the Kac-Moody current is given in terms of a certain soft graviton operator on the boundary of ℐ$$ \mathrm{\mathcal{I}} $$.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e1235276e3b753c3c7a04436bb6e6728e4647155

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Soft sub-leading divergences in Yang-Mills amplitudes (2014, neutral): “Recently soft limits have been investigated from the point of view of asymptotic symmetries of flat space [1, 2, 3], in particular Weinberg’s soft graviton theorem has been derived from the action of the super-translations of the BMS group on the gravitational S-matrix.”
Symmetries and charges of general relativity at null boundaries (2018, background): “They should facilitate further investigations of whether horizon symmetries and conservation laws in black hole spacetimes play a role in the information loss problem, as suggested by Hawking, Perry, and Strominger.”
Celestial Holography (2021, background): “The celestial holography program is rooted in the interesting observation [30,31] that the perturbative gravitational S-matrix provides additional guidance in addressing this question.”
Local subsystems in gauge theory and gravity (2016, background): “Much recent work has focused on asymptotic symmetries of Yang-Mills theories [59, 60] and gravity [61, 62].”
New symmetries of massless QED (2014, methodology): “For example Weinberg’s soft graviton theorem [20, 21] is equivalent to a symmetry of the S-matrix generated by a certain diagonal subgroup [2] of the product of BMS [22] supertranslations acting on past and future null infinity, I + and I .”
Holographic symmetry algebras for gauge theory and gravity (2021, background): “Only very recently [3,4], using soft theorems from quantum field theory, was it shown that there are an infinite number of non-trivial symmetries of GR with associated conserved charges.”
Evidence for a New Soft Graviton Theorem (2014, methodology): “Another follows the path of [2, 3] to Weinberg’s theorem in explicitly constructing the generators of the conjectured superrotation Virasoro symmetries and rewriting the invariance of the Smatrix in the form of a soft theorem.”
Lectures on celestial amplitudes (2021, background): “The final ingredient is an insight by Strominger [7] that we can impose an antipodal matching condition across spatial infinity.”
4D scattering amplitudes and asymptotic symmetries from 2D CFT (2016, methodology): “We then utilize the extended BMS algebra [71] to derive the CFT2 Ward identity associated with “super-translations” [25, 26], and we confirm that they correspond to the leading Weinberg soft theorem for gravitons [28, 29].”
Asymptotic symmetries and subleading soft graviton theorem (2014, methodology): “Identifying the null generators of I and I− through I|u=−∞ = I|v=+∞ = i, the group is defined by the conditions [11]:”
Notes on the BMS group in three dimensions: I. Induced representations (2014, background): “There has recently been a lot of interest in this group in the context of gravitational scattering theory and soft graviton theorems [13–16] (see also [17] for a novel approach in the framework of conformal Carroll groups).”
Superrotation charge and supertranslation hair on black holes (2016, methodology): “Supertranslation (superrotation) charge conservation equates the total incoming energy at each angle to the total outgoing energy (angular momentum) at the opposing angle [2, 26].”
New gravitational memories (2015, background): “y Hawking, is constrained only by energymomentum, angular momentum and charge conservation. Imposing the inﬁnity of conservation laws (7.7) (together with a second inﬁnity arising from BMS invariance [24]) will greatly constrain the outgoing Hawking radiation. These constraints follow solely from lo”
Asymptotic symmetries and electromagnetic memory (2015, background): “The first step, linking soft factors and symmetries, was motivated by concurrent success connecting the leading soft factors with supertranslations [8, 9] and an asymptotic large U(1) gauge symmetry [10].”
BMS supertranslations and Weinberg’s soft graviton theorem (2014, positive): “The Ward identities following from the diagonal BMS supertranslations were expressed in [2] in terms of data at null inﬁnity, namely the Bondi news representing gravitational radiation together with certain infrared modes.”
2D Kac-Moody symmetry of 4D Yang-Mills theory (2015, background): “The asymptotic symmetries of gravity (or QED) are spontaneously broken in the perturbative vacuum and the soft gravitons (or photons) were shown to be the resulting Goldstone bosons [7,8,10].”
Asymptotic symmetries of QED and Weinberg’s soft photon theorem (2015, background): “Recently a new perspective on asymptotic symmetries and infrared effects in quantum field theories on (asymptotically) flat space times has emerged [1, 2, 3, 4, 5].”