On BMS invariance of gravitational scattering

Abstract

BMS + transformations act nontrivially on outgoing gravitational scattering data while preserving intrinsic structure at future null infinity (I + ). BMS − transformations similarly act on ingoing data at past null infinity (I − ). In this paper we apply -within a suitable finite neighborhood of the Minkowski vacuum -results of Christodoulou and Klainerman to link I + to I − and thereby identify "diagonal" elements BMS 0 of BMS + ×BMS − . We argue that BMS 0 is a nontrivial infinite-dimensional symmetry of both classical gravitational scattering and the quantum gravity S-matrix. It implies the conservation of net accumulated energy flux at every angle on the conformal S 2 at I. The associated Ward identity is shown to relate S-matrix elements with and without soft gravitons. Finally, BMS 0 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.

The double copy structure of soft gravitons

“…This is an added complication when investigating higher-point amplitudes. Another interesting problem to address is the implications of our results for the possible relation between the asymptotic symmetries of gauge theories [15,30] and gravity [5,6]. These and other issues will be studied elsewhere.…”

“…More recently, there has been a renewed interest in these results stemming from the realization that Weinberg's soft-graviton theorem can be regarded as the Ward identity associated with the symmetries of the gravitational theory at null infinity [5,6]. This has led to the formulation of a new soft-graviton theorem including next-to-leading and next-to-next-to-leading order corrections which have a universal expression in terms of the angular momentum of the hard particles [7].…”

Asymptotic symmetries, holography and topological hair

“…Considerable progress has been made in this regard by the discovery that the associated large diffeomorphisms and gauge transformations arise as soft limits of physical gravitational and gauge fields emerging from scattering processes [5][6][7][8][9][10][11][12][13][14][15], as captured by the Weinberg Soft Theorems [16][17][18][19][20]. The infinite-dimensional AS then describe the soft field dressing of a hard process, and are sensitive to the passage of charge/energy-momentum as a function of angle, through "memory" effects [21][22][23][24][25][26][27][28][29][30].…”

From U(1) to E8: soft theorems in supergravity amplitudes

“…The authors of ref. [19] 1 For the understanding on soft behaviors from other symmetry principles see [6][7][8][9][10][11].…”