The SAGEX review on scattering amplitudes Chapter 11: Soft Theorems and Celestial Amplitudes

Abstract

The soft limits of scattering amplitudes have been extensively studied due to their essential role in the computation of physical observables in collider physics. The universal factorisation that occurs in these kinematic limits has been shown to be related to conservation laws associated with asymptotic, or large, gauge symmetries. This connection has led to a deeper understanding of the symmetries of gauge and gravitational theories and to a reformulation of scattering amplitudes in a basis of boost eigenstates which makes manifest the two-dimensional global conformal symmetry of the celestial sphere. The recast, or celestial, amplitudes possess many of the properties of conformal field theory correlation functions which has suggested a path towards a holographic description of asymptotically flat spacetimes. In this review we consider these interconnected developments in our understanding of soft theorems, asymptotic symmetries and conformal field theory with a focus on the structure and symmetries of the celestial amplitudes and their holographic interpretation.

Towards higher-spin holography in flat space

“…Quadratic relations (2.3), (2.5) vanish when evaluated on the singleton representation of so(d − 1, 2), that is the representation carried by the boundary field theory. 6 Thus, the higher-spin algebra can be equivalently understood as the universal enveloping algebra U(g) evaluated on the singleton representation. This property can be used to identify the singleton representation once the higher-spin algebra is known.…”

“…In recent years significant interest was drawn to flat space holography. For reviews on the subject we refer the reader to [1][2][3][4][5][6]. There are different approaches to flat space holography, but all of them acknowledge the central role of the (extended) BMS symmetry [7,8] -or, equivalently, the conformal Carroll symmetry [9] -as the symmetry underlying the dual boundary dynamics [10][11][12][13][14][15][16][17][18].…”

Chiral higher-spin holography in flat space: the Flato-Fronsdal theorem and lower-point functions

“…The existence of the aforementioned automorphism implies that when trying to achieve invariance of the intertwining kernel under spin-3 symmetry, we are free to change signs of ( J11 ) 2 at our convenience. In particular, if the action of the higher-spin algebra on the second singleton is supplemented with (A.9), then the action of ( J11 ) 2 on the tensor product of singletons becomes a 4 1 − a 4 2 . One can then see that the invariance of the kernel leads to α 2 = 2.…”

“…Flat space holography attracted considerable attention in recent years, see e.g. [1][2][3][4] for review. Despite significant progress in this area, explicit holographically dual pairs with both theories independently defined are lacking, see, however, recent suggestions [5][6][7].…”

A comment on loop corrections to the celestial stress tensor

“…While it is perhaps not surprising in hindsight that the IR behavior of scattering [3][4][5] is imprinted on the large distance, long timescale modes on the boundary [6][7][8], the concrete proposal of an equivalence between asymptotic symmetries and soft theorems [9,10] has provided an interesting avenue to explore extensions of the asymptotic symmetry group. In this story, the subleading soft graviton plays a particularly important role because it encodes a Virasoro symmetry of the S-matrix [11][12][13][14], motivating the celestial hologram [15][16][17][18].…”