Infinite Set of Soft Theorems in Gauge-Gravity Theories as Ward-Takahashi Identities

Abstract

We show that the soft photon, gluon, and graviton theorems can be understood as the Ward-Takahashi identities of large gauge transformation, i.e., diffeomorphism that does not fall off at spatial infinity. We found infinitely many new identities which constrain the higher order soft behavior of the gauge bosons and gravitons in scattering amplitudes of gauge and gravity theories. Diagrammatic representations of these soft theorems are presented. DOI: 10.1103/PhysRevLett.120.201601 Introduction.-The last few decades have witnessed a remarkable synergy between particle physics and cosmology. While the objects of interest are vastly different, the tools to study them often share a great deal of similarity. A recent example of this synergy is the notion of "cosmological collider physics" [1]. Just as we extract particles' interactions from scattering in colliders, we can extract the interactions governing the early Universe from the correlations of primordial fluctuations that seed cosmic structure formation. Thus, N-point corrections (N ≥ 3) of the curvature perturbation (also known as non-Gaussianities) play a similar role as scattering amplitudes in particle physics.Another commonality between particle physics and cosmology is that they are both populated with a myriad of theories, and the challenge is to zero in on the right ones. In this regard, results based on symmetries are especially powerful as they allow us to test and discriminate broad classes of theories in a model-independent manner. Soft theorems which govern the behavior of scattering amplitudes or correlation functions when one or more of the momenta approach zero are a prominent example. The subject of soft theorems has a long history in particle physics, dating back to the early studies of the soft pion theorem. The equivalence between the soft photon theorem [2,3] and large gauge transformation has already been noted long ago by Ferrari and Picasso [4] (see, also, [5]), where the leading and subleading soft theorems were shown to follow from the Ward-Takahashi (WT) identity of linear transformation which survives after Lorenz gauge fixing.

Scattering of spinning black holes from exponentiated soft factors

“…[77] where we have used that p 2 = m 2 for a null momentum transfer k. Finally, we note that in the classical limit k → 0 we retrieve the spin tensor (B.4) as the covariant-SSC one. 12 The conjugation rule between the incoming and outgoing states in the massive spinor-helicity formalism amounts to lowering and raising the little-group indices, as indicated by the completeness relation in eq. (2.10).…”

Strolling along gravitational vacua

“…Our result could possibly be matched with an extension of the BMS group containing Diff(S 2 ). One such extension was proposed in [24], but especially the symmetries of [25] (see also [26]) -obtained by a correspondence to an infinite tower of soft theorems -appear to be identical to those of our setup.…”

Infinite Towers of Supertranslation and Superrotation Memories

“…Their existence go handin-hand. Now, the existence of at least one tower of soft theorems was recently established [11]. More precisely, the soft graviton identities written in [11] can be recognized as the Ward identitites of momentum and current multipole symmetries, which are associated with conserved multipole charges at spatial infinity [10].…”