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Title: Prescriptive unitarity

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [3]
  1. Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Univ. of Copenhagen (Denmark). The Niels Bohr Inst.
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States); Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics
  3. Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Univ. of California, Davis, CA (United States)
+ Show Author Affiliations

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 (SYM), 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.

Research Organization:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP)
Grant/Contract Number:
SC0011632; PHY-1125915
OSTI ID:
1426866
Journal Information:
Journal of High Energy Physics (Online), Vol. 2017, Issue 6; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 47 works
Citation information provided by
Web of Science

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Heptagons from the Steinmann Cluster Bootstrap text January 2017
Motivic amplitudes and cluster coordinates text January 2014
Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes text January 2007
Dual Superconformal Invariance, Momentum Twistors and Grassmannians text January 2009
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More on the duality correlators/amplitudes text January 2010
Notes on the scattering amplitude / Wilson loop duality text January 2010
All tree-level amplitudes in massless QCD text January 2010
Review of AdS/CFT Integrability: An Overview text January 2010
One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts text January 2011
From polygons and symbols to polylogarithmic functions text January 2011
Uniqueness of two-loop master contours text January 2012
ABJM amplitudes and the positive orthogonal grassmannian text January 2013
A Two-Loop Five-Gluon Helicity Amplitude in QCD text January 2013
Ambitwistor strings and the scattering equations text January 2013
Bootstrapping an NMHV amplitude through three loops text January 2014
Feynman integrals and iterated integrals on moduli spaces of curves of genus zero preprint January 2014
Amplituhedron cells and Stanley symmetric functions preprint January 2014
Logarithmic Singularities and Maximally Supersymmetric Amplitudes preprint January 2014
Non-Planar On-Shell Diagrams preprint January 2015
Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM text January 2015
Scattering Equations and Feynman Diagrams text January 2015
A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory text January 2015
Integration Rules for Loop Scattering Equations text January 2015
One-loop amplitudes on the Riemann sphere text January 2015
Evidence for a Nonplanar Amplituhedron text January 2015
Gravity On-shell Diagrams text January 2016
Adaptive Integrand Decomposition in parallel and orthogonal space text January 2016
Heptagons from the Steinmann Cluster Bootstrap text January 2016
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Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes text January 1994
Progress in One-Loop QCD Computations text January 1996
New Recursion Relations for Tree Amplitudes of Gluons text January 2004
Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops text January 1996
On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences text January 1998
Enumeration of totally positive Grassmann cells preprint January 2003

Cited By (13)

Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case journal January 2019
Rooting out letters: octagonal symbol alphabets and algebraic number theory journal February 2020
A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons journal September 2019
The cosmic Galois group and extended Steinmann relations for planar N $$ \mathcal{N} $$ = 4 SYM amplitudes text January 2019
A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons text January 2019
The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes text January 2019
Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case text January 2019
All-Helicity Symbol Alphabets from Unwound Amplituhedra text January 2017
A first look at two-loop five-gluon scattering in QCD text January 2017
Rationalizing Loop Integration text January 2018
The two-loop five-point amplitude in $\mathcal N=8$ supergravity text January 2019
The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes text January 2019
Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops text January 2019

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS