Constructing Gravity Amplitudes from Real Soft and Collinear Factorisation

Abstract

Soft and collinear factorisations can be used to construct expressions for amplitudes in theories of gravity. We generalise the "half-soft" functions used previously to "soft-lifting" functions and use these to generate tree and one-loop amplitudes. In particular we construct expressions for MHV tree amplitudes and the rational terms in one-loop amplitudes in the specific context of N=4 supergravity. To completely determine the rational terms collinear factorisation must also be used. The rational terms for N=4 have a remarkable diagrammatic interpretation as arising from algebraic link diagrams.

18 pages, axodraw, Proof of eq. 4.3 added

References in corpus (5)

• New Relations for Gauge-Theory Amplitudes
• Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
• The No-Triangle Hypothesis for N=8 Supergravity
• Explicit Cancellation of Triangles in One-loop Gravity Amplitudes
• Inverse Soft Factors and Grassmannian Residues

Cited by in corpus (12)

• Evidence for a New Soft Graviton Theorem
• Loop Corrections to Soft Theorems in Gauge Theories and Gravity
• Subleading soft theorem in arbitrary dimension from scattering equations
• BCJ duality and the double copy in the soft limit
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• Subleading Soft Factor for String Disk Amplitudes
• Generating All Tree Amplitudes in N=4 SYM by Inverse Soft Limit
• $n$-point amplitudes with a single negative-helicity graviton
• Cancelling the U(1) Anomaly in the S-matrix of N=4 Supergravity
• One-loop four-graviton amplitudes in N=4 supergravity models
• Soft Theorems from Effective Field Theory
• Complex Factorisation and Recursion for One-Loop Amplitudes