Infinite soft theorems from gauge symmetry

Abstract

In this letter we show that the soft behaviour of photons and graviton amplitudes, after projection, can be determined to infinite order in soft expansion via ordinary on-shell gauge invariance. In particular, as one of the particle's momenta becomes soft, gauge invariance relates the non-singular diagrams of an n-point amplitude to that of the singular ones up to possible homogeneous terms. We demonstrate that with a particular projection of the soft-limit, the homogeneous terms do not contribute, and one arrives at an infinite soft theorem. This reproduces the result recently derived from the Ward identity of large gauge transformations. We also discuss the modification of these soft theorems due to the presence of higher-dimensional operators.

Asymptotic charges in massless QED revisited: a view from spatial infinity

“…As it turns out, from the side of soft theorems, a complimentary puzzle already existed: (B) In [6,7], it was shown that in fact for tree level scattering amplitudes in QED, there do exist an infinity of soft theorems. From the perspective of these soft theorems, a natural question to ask would be, just as leading and sub-leading soft theorems are Ward identities for certain asymptotic symmetries.…”

“…As a first example of this kind, in this section we focus on 2,2 F ru (x) and write the corresponding charge Q + 2 [ǫ + ] as an integral over I + as a functional of the free data. We will refer to this charge as sub-subleading charge as the corresponding Ward identities will turn out to be equivalent to the ("projected" [7]) sub-subleading soft photon theorem for tree-level QED. 6 That is we would like to evaluate,…”

“…We would now like to show that if we assume Q + 2 [ǫ + ] = Q − 2 [ǫ − ] then the corresponding Ward identity is equivalent to the sub-subleading soft photon theorem in tree level scattering amplitudes [6,7].…”

Soft theorems and the KLT-relation

“…Recently, infinite partial soft theorems were discussed in refs. [48,49]. Understanding the connection between our results and the infinite partial soft theorems would be illuminating.…”

Notes on the gravitational, electromagnetic and axion memory effects

“…Recently, the memory effect in cosmological setup has been investigated [6,7,8,9,10,11,12]. Other than the experimental aspect, the memory effect is theoretically interesting because it has a strong connection to the notion such as the soft graviton theorem and asymptotic symmetry [13,14,15,16,17,18,19].…”