Soft Photon and Graviton Theorems in Effective Field Theory

105

Abstract:We analyze scattering amplitudes with one soft external graviton and arbitrary number of other finite energy external states carrying arbitrary mass and spin to subsubleading order in the momentum of the soft graviton. Our result can be expressed as the sum of a universal part that depends only on the amplitude without the soft graviton and not the other details of the theory and a non-universal part that depends on the amplitude without the soft graviton, and the two and three point functions of the theory. For tree amplitudes our results are valid in all space-time dimensions while for loop amplitudes, infrared divergences force us to restrict our analysis to space time dimensions five or more. With this restriction the results are valid to all orders in perturbation theory. Our results agree with known results in quantum field theories and string theory.

“…This is identical to (4.36), in agreement with [57]. For specific helicity configurations, the nature of soft theorems can be completely governed by the non-universal terms.…”

Section: Jhep10(2017)065supporting

confidence: 84%

Section: Jhep10(2017)065supporting

confidence: 77%

Section: Acknowledgmentsmentioning

confidence: 95%

Section: Four Dimensional Quantum Field Theories With Higher Derivatimentioning

confidence: 99%

“…Therefore (4.28) reduces to (4.24). In order to compare this with the result of [57] we need to convert (4.24) to the spinor helicity notation (see e.g. [61,62] for a review).…”

Section: Jhep10(2017)065mentioning

confidence: 99%

See 3 more Smart Citations

Sub-subleading soft graviton theorem in generic theories of quantum gravity

Laddha

Sen

2017

105

Testing subleading multiple soft graviton theorem for CHY prescription

Chakrabarti

Kashyap

Sahoo

et al. 2018

In arXiv:1707.06803 we derived the subleading multiple soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. In this paper we verify this explicitly using the CHY formula for tree level scattering amplitudes of arbitrary number of gravitons in Einstein gravity. We pay special care to fix the signs of the amplitudes and resolve an apparent discrepancy between our general results in arXiv:1707.06803 and previous results on soft graviton theorem from CHY formula.

Multiloop soft theorem for gravitons and dilatons in the bosonic string

Vecchia

Marotta

Mojaza

2019

We construct, in the closed bosonic string, the multiloop amplitude involving N tachyons and one massless particle with 26 − D compactified directions, and we show that at least for D > 4, the soft behaviors of the graviton and dilaton satisfy the same soft theorems as at the tree level, up to one additional term at the subsubleading order, which can only contribute to the dilaton soft behavior and which we show is zero at least at one loop. This is possible, since the infrared divergences due to the non-vanishing tachyon and dilaton tadpoles do not depend on the number of external particles and are therefore the same both in the amplitude with the soft particle and in the amplitude without the soft particle. Therefore this leaves unchanged the soft operator acting on the amplitude without the soft particle. The additional infrared divergence appearing for D ≤ 4 depend on the number of external legs and must be understood on their own.