Subleading Soft Theorem for Multiple Soft Gravitons
Subhroneel Chakrabarti, Sitender Pratap Kashyap, Biswajit Sahoo, Ashoke Sen, Mritunjay Verma
TL;DR
This paper derives the subleading soft graviton theorem for arbitrary numbers of soft gravitons in a general quantum gravity framework, valid to all orders in perturbation theory for six or more non-compact dimensions and at tree level for five or fewer dimensions. The authors build soft-graviton couplings by covariantizing the 1PI action, compute explicit vertices and propagators, and show that the amplitude factorizes into leading soft factors acting on the hard amplitude plus subleading, angular-momentum- and contact-term corrections. Consistency checks confirm gauge invariance and off-shell insensitivity, and the results are cross-validated against known double-soft results from CHY and BCFW approaches, with complete generalization to an arbitrary number $M$ of soft gravitons. The work deepens understanding of soft-graviton universality and provides a framework applicable to broad classes of theories with gravity, including implications for infrared structure and asymptotic symmetries.
Abstract
We derive the subleading 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. Our results are valid to all orders in perturbation theory when the number of non-compact space-time dimensions is six or more, but only for tree amplitudes for five or less non-compact space-time dimensions due to enhanced contribution to loop amplitudes from the infrared region.