Prescriptive Unitarity

Abstract

We introduce a prescriptive approach to generalized unitarity, resulting in a strictly-diagonal basis of loop integrands with coefficients given by specifically-tailored residues in field theory. We illustrate the power of this strategy in the case of planar, maximally supersymmetric Yang-Mills theory, where we construct closed-form representations of all ($n$-point N${}^k$MHV) scattering amplitudes through three loops. The prescriptive approach contrasts with the ordinary description of unitarity-based methods by avoiding any need for linear algebra to determine integrand coefficients. We describe this approach in general terms as it should have applications to many quantum field theories, including those without planarity, supersymmetry, or massless spectra defined in any number of dimensions.

59 pages, 129 figures, 2 tables

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• All tree-level amplitudes in massless QCD
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• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
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• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
• Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Embedding Feynman Integral (Calabi-Yau) Geometries in Weighted Projective Space
• Duals of Feynman Integrals, I: Differential Equations
• Rationalizing Loop Integration
• Duals of Feynman Integrals, 2: Generalized Unitarity
• Implications of the Landau Equations for Iterated Integrals
• Cutting Deep Into The Amplituhedron
• Cosmology meets cohomology
• Scalar QED as a toy model for higher-order effects in classical gravitational scattering
• MHV scattering of gluons and gravitons in chiral strong fields
• All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• On Epsilon Factorized Differential Equations for Elliptic Feynman Integrals
• Amplitudes at Infinity
• Manifestly Dual-Conformal Loop Integration
• All-Helicity Symbol Alphabets from Unwound Amplituhedra
• Dual conformal invariance for form factors
• Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function
• UV cancelations in gravity loop integrands
• Building Bases of Loop Integrands
• Algebraic branch points at all loop orders from positive kinematics and wall crossing
• The SAGEX Review on Scattering Amplitudes, Chapter 7: Positive Geometry of Scattering Amplitudes
• Bootstrapping elliptic Feynman integrals using Schubert analysis
• Prescriptive Unitarity with Elliptic Leading Singularities
• On $\epsilon$-factorised bases and pure Feynman integrals
• An Elliptic Yangian-Invariant, `Leading Singularity'
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Rooting Out Letters: Octagonal Symbol Alphabets and Algebraic Number Theory
• Gravity loop integrands from the ultraviolet
• Multi-Particle Amplitudes from the Four-Point Correlator in Planar N=4 SYM
• Non-planar BCFW Grassmannian Geometries
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• Maximal transcendental weight contribution of scattering amplitudes
• Poles At Infinity in On-shell Diagrams
• Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals
• Illustrations of Integrand-Basis Building at Two Loops
• On the finite basis topologies for multi-loop high-multiplicity Feynman integrals
• All Two-Loop, Color-Dressed, Six-Point Amplitude Integrands in sYM
• Locally Finite Observables in sYM
• The spectrum of Feynman-integral geometries at two loops
• Integrands of Less-Supersymmetric Yang-Mills at One Loop