Absence of Triangles in Maximal Supergravity Amplitudes

Abstract

From general arguments, we show that one-loop n-point amplitudes in colourless theories satisfy a new type of reduction formula. These lead to the existence of cancellations beyond supersymmetry. Using such reduction relations we prove the no-triangle hypothesis in maximal supergravity by showing that in four dimensions the n-point graviton amplitude contain only scalar box integral functions. We also discuss the reduction formulas in the context of gravity amplitudes with less and no supersymmetry.

23 pages, RevTeX4 format. v2: Expanded version with a new section providing some extra background material and an overview of the general arguments. Minors typos have been corrected. Version to be published

Cited by in corpus (55)

• What is the Simplest Quantum Field Theory?
• A Duality For The S Matrix
• The Ultraviolet Behavior of N=8 Supergravity at Four Loops
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• The S-Matrix in Twistor Space
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
• Classical Gravity from Loop Amplitudes
• Towards one-loop SYM amplitudes from the pure spinor BRST cohomology
• Loop amplitudes in gauge theories: modern analytic approaches
• Proof of Gravity and Yang-Mills Amplitude Relations
• String-inspired BCJ numerators for one-loop MHV amplitudes
• A simple approach to counterterms in N=8 supergravity
• The Tree Formula for MHV Graviton Amplitudes
• Scattering amplitudes: the most perfect microscopic structures in the universe
• Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory
• Multiparticle one-loop amplitudes and S-duality in closed superstring theory
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• R^4 counterterm and E7(7) symmetry in maximal supergravity
• On-shell superamplitudes in N<4 SYM
• Tropical Amplitudes
• BCJ duality and double copy in the closed string sector
• No triangles on the moduli space of maximally supersymmetric gauge theory
• On the Structure of Supersymmetric Sums in Multi-Loop Unitarity Cuts
• Tree-Level Amplitudes in N=8 Supergravity
• Simplicity in the Structure of QED and Gravity Amplitudes
• Unraveling L_{n,k}: Grassmannian Kinematics
• On powercounting in perturbative quantum gravity theories through color-kinematic duality
• Yang-Mills amplitude relations at loop level from non-adjacent BCFW shifts
• From maximal to minimal supersymmetry in string loop amplitudes
• The Next-to-Simplest Quantum Field Theories
• Loop amplitudes monodromy relations and color-kinematics duality
• One-loop four-graviton amplitudes in N=4 supergravity models
• UV cancelations in gravity loop integrands
• Higher-loop amplitudes in the non-minimal pure spinor formalism
• Building Bases of Loop Integrands
• The Unitarity Method using a Canonical Basis Approach
• String-inspired representations of photon/gluon amplitudes
• Perturbative expansion of N<8 Supergravity
• Gravitino Interactions from Yang-Mills Theory
• Loop amplitudes in maximal supergravity with manifest supersymmetry
• A super MHV vertex expansion for N=4 SYM theory
• Local BCJ numerators for ten-dimensional SYM at one loop
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Complex Factorisation and Recursion for One-Loop Amplitudes
• Constructing Gravity Amplitudes from Real Soft and Collinear Factorisation
• Compact QED Tree-Level Amplitudes From Dressed BCFW Recursion Relations
• Gravity loop integrands from the ultraviolet
• Obtaining One-loop Gravity Amplitudes Using Spurious Singularities
• Ultraviolet divergences in maximal supergravity from a pure spinor point of view
• A Note on Single Soft Scalar Emission of $\mathcal{N}=8$ SUGRA and $E_{7(7)}$ Symmetry
• Rational Terms in Theories with Matter
• Photon-Graviton Amplitudes from the Effective Action
• Integrands of Less-Supersymmetric Yang-Mills at One Loop