Graphs, determinants and gravity amplitudes

Abstract

We apply the matrix-tree theorem to establish a link between various diagrammatic and determinant expressions, which naturally appear in scattering amplitudes of gravity theories. Using this link we are able to give a general graph-theoretical formulation for the tree-level maximally-helicity-violated gravity amplitudes. Furthermore, we use the link to prove two identities for half-soft functions of gravity amplitudes. Finally we recast the diagrammatic formulation of one-loop rational part of $\mathcal{N}=4$ supergravity into a matrix form.

19 pages, 3 figures

References in corpus (5)

• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Minimal Basis for Gauge Theory Amplitudes
• Three-Loop Superfiniteness of N=8 Supergravity
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• New Identities among Gauge Theory Amplitudes

Cited by in corpus (25)

• The Kinematic Algebras from the Scattering Equations
• Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame
• Conformal and Einstein gravity from twistor actions
• Unraveling conformal gravity amplitudes
• Conformal higher spin scattering amplitudes from twistor space
• Celestial $w_{1+\infty }$ Symmetries from Twistor Space
• Cancelling the U(1) Anomaly in the S-matrix of N=4 Supergravity
• Conformal Higher Spin Theory and Twistor Space Actions
• Superstring Amplitudes as a Mellin Transform of Supergravity
• Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism
• Kinematic numerators from the worldsheet: cubic trees from labelled trees
• Worldsheet factorization for twistor-strings
• A Link Representation for Gravity Amplitudes
• Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism
• A graphic approach to gauge invariance induced identity
• A String Deformation of the Parke-Taylor Factor
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Note on Identities Inspired by New Soft Theorems
• Constructing EYM amplitudes by inverse soft limit
• Evaluating EYM amplitudes in four dimensions by refined graphic expansion
• Gravity Amplitudes from n-Space
• Weighted Laplacians, cocycles and recursion relations
• Advanced tools for basis decompositions of genus-one string integrals
• Pure connection formalism for gravity: Recursion relations
• A note on multi-trace EYM amplitudes in four dimensions