Loop corrections to soft theorems in gauge theories and gravity
Song He (School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, U.S.A., Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada); Yu-tin Huang (School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, U.S.A., Department of Physics and Astronomy, National Taiwan University, Taipei, 10617, Taiwan, R.O.C.); Congkao Wen (Centre for Research in String Theory, Department of Physics, Queen Mary University of London, Mile End Road, London, E1 4NS, U.K.)
In this paper, we study loop corrections to the recently proposed new soft theorems of Cachazo and Strominger [1], for both gravity and gauge theory amplitudes. We first review the proof of its tree-level validity based on BCFW recursion relations, which also establishes an infinite series of universals soft functions for MHV amplitudes, and a generalization to supersymmetric cases. For loop corrections, we focus on infrared finite, rational amplitudes at one loop, and apply recursion relations with boundary or double-pole contributions. For all-plus amplitudes, we prove that the subleading soft theorems are exact to all multiplicities for gauge theory and up to 12-points for gravity amplitudes. For single-minus amplitudes, while the subleading soft theorems are again exact for the minus-helicity soft leg, for plus-helicity loop corrections are required. Using recursion relations, we identify the source of such mismatch as stemming from the special contribution containing double poles, and obtain the all multiplicity one-loop corrections to the subleading soft behavior in Yang-Mills theory. We also comment on the derivation of soft theorems using BCFW recursion in arbitrary dimensions.
