Local integrand representations of all two-loop amplitudes in planar SYM
Abstract
We use generalized unitarity at the integrand-level to directly construct local, manifestly dual-conformally invariant formulae for all two-loop scattering amplitudes in planar, maximally supersymmetric Yang-Mills theory (SYM). This representation separates contributions into manifestly finite and manifestly divergent terms — in a way that renders all infrared-safe observables (including ratio functions) calculable without any need for regulation. These results perfectly match the all-loop BCFW recursion relations, to which we provide a closed-form solution valid through two-loop-order. Finally, we describe and document a Mathematica package which implements these results, available as part of this work’s source files on the arXiv.
- Authors:
-
- Univ. of Copenhagen (Denmark). The Niels Bohr Inst.
- California Institute of Technology (CalTech), Pasadena, CA (United States)
- Publication Date:
- Research Org.:
- California Institute of Technology (CalTech), Pasadena, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1600669
- Grant/Contract Number:
- SC0011632
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 8; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Supersymmetric gauge theory; Scattering Amplitudes; 1/N Expansion
Citation Formats
Bourjaily, Jacob L., and Trnka, Jaroslav. Local integrand representations of all two-loop amplitudes in planar SYM. United States: N. p., 2015.
Web. doi:10.1007/JHEP08(2015)119.
Bourjaily, Jacob L., & Trnka, Jaroslav. Local integrand representations of all two-loop amplitudes in planar SYM. United States. https://doi.org/10.1007/JHEP08(2015)119
Bourjaily, Jacob L., and Trnka, Jaroslav. Tue .
"Local integrand representations of all two-loop amplitudes in planar SYM". United States. https://doi.org/10.1007/JHEP08(2015)119. https://www.osti.gov/servlets/purl/1600669.
@article{osti_1600669,
title = {Local integrand representations of all two-loop amplitudes in planar SYM},
author = {Bourjaily, Jacob L. and Trnka, Jaroslav},
abstractNote = {We use generalized unitarity at the integrand-level to directly construct local, manifestly dual-conformally invariant formulae for all two-loop scattering amplitudes in planar, maximally supersymmetric Yang-Mills theory (SYM). This representation separates contributions into manifestly finite and manifestly divergent terms — in a way that renders all infrared-safe observables (including ratio functions) calculable without any need for regulation. These results perfectly match the all-loop BCFW recursion relations, to which we provide a closed-form solution valid through two-loop-order. Finally, we describe and document a Mathematica package which implements these results, available as part of this work’s source files on the arXiv.},
doi = {10.1007/JHEP08(2015)119},
journal = {Journal of High Energy Physics (Online)},
number = 8,
volume = 2015,
place = {United States},
year = {Tue Aug 25 00:00:00 EDT 2015},
month = {Tue Aug 25 00:00:00 EDT 2015}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 44 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions
journal, August 2014
- Basso, Benjamin; Sever, Amit; Vieira, Pedro
- Journal of High Energy Physics, Vol. 2014, Issue 8
A cluster bootstrap for two-loop MHV amplitudes
journal, February 2015
- Golden, John; Spradlin, Marcus
- Journal of High Energy Physics, Vol. 2015, Issue 2
Multivariate residues and maximal unitarity
journal, December 2013
- Søgaard, Mads; Zhang, Yang
- Journal of High Energy Physics, Vol. 2013, Issue 12
Conformal properties of four-gluon planar amplitudes and Wilson loops
journal, May 2008
- Drummond, J. M.; Korchemsky, G. P.; Sokatchev, E.
- Nuclear Physics B, Vol. 795, Issue 1-2
Bootstrapping an NMHV amplitude through three loops
journal, October 2014
- Dixon, Lance J.; von Hippel, Matt
- Journal of High Energy Physics, Vol. 2014, Issue 10
Hexagon functions and the three-loop remainder function
journal, December 2013
- Dixon, Lance J.; Drummond, James M.; von Hippel, Matt
- Journal of High Energy Physics, Vol. 2013, Issue 12
Integrand-level reduction of loop amplitudes by computational algebraic geometry methods
journal, September 2012
- Zhang, Yang
- Journal of High Energy Physics, Vol. 2012, Issue 9
Analytic result for the two-loop six-point NMHV amplitude in $ \mathcal{N} = {4} $ super Yang-Mills theory
journal, January 2012
- Dixon, Lance J.; Drummond, James M.; Henn, Johannes M.
- Journal of High Energy Physics, Vol. 2012, Issue 1
New recursion relations for tree amplitudes of gluons
journal, May 2005
- Britto, Ruth; Cachazo, Freddy; Feng, Bo
- Nuclear Physics B, Vol. 715, Issue 1-2
Multiloop Integrals in Dimensional Regularization Made Simple
journal, June 2013
- Henn, Johannes M.
- Physical Review Letters, Vol. 110, Issue 25
The Amplituhedron
journal, October 2014
- Arkani-Hamed, Nima; Trnka, Jaroslav
- Journal of High Energy Physics, Vol. 2014, Issue 10
Analytic results for two-loop master integrals for Bhabha scattering I
journal, November 2013
- Henn, Johannes M.; Smirnov, Vladimir A.
- Journal of High Energy Physics, Vol. 2013, Issue 11
Magic identities for conformal four-point integrals
journal, January 2007
- Drummond, James M.; Henn, Johannes; Smirnov, Vladimir A.
- Journal of High Energy Physics, Vol. 2007, Issue 01
Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions
journal, May 2014
- Henn, Johannes M.; Melnikov, Kirill; Smirnov, Vladimir A.
- Journal of High Energy Physics, Vol. 2014, Issue 5
Into the amplituhedron
journal, December 2014
- Arkani-Hamed, Nima; Trnka, Jaroslav
- Journal of High Energy Physics, Vol. 2014, Issue 12
Bootstrapping six-gluon scattering in planar N=4 super-Yang-Mills theory
conference, August 2014
- Dixon, Lance; Drummond, James; Duhr, Claude
- Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2014)
Bootstrapping the three-loop hexagon
journal, November 2011
- Dixon, Lance J.; Drummond, James M.; Henn, Johannes M.
- Journal of High Energy Physics, Vol. 2011, Issue 11
Spacetime and Flux Tube -Matrices at Finite Coupling for Supersymmetric Yang-Mills Theory
journal, August 2013
- Basso, Benjamin; Sever, Amit; Vieira, Pedro
- Physical Review Letters, Vol. 111, Issue 9
Generalized unitarity and one-loop amplitudes in super-Yang–Mills
journal, October 2005
- Britto, Ruth; Cachazo, Freddy; Feng, Bo
- Nuclear Physics B, Vol. 725, Issue 1-2
What is the simplest quantum field theory?
journal, September 2010
- Arkani-Hamed, Nima; Cachazo, Freddy; Kaplan, Jared
- Journal of High Energy Physics, Vol. 2010, Issue 9
Eliminating spurious poles from gauge-theoretic amplitudes
journal, May 2013
- Hodges, Andrew
- Journal of High Energy Physics, Vol. 2013, Issue 5
Dual superconformal symmetry of scattering amplitudes in super-Yang–Mills theory
journal, March 2010
- Drummond, J. M.; Henn, J.; Korchemsky, G. P.
- Nuclear Physics B, Vol. 828, Issue 1-2
Fusing gauge theory tree amplitudes into loop amplitudes
journal, February 1995
- Bern, Zvi; Dixon, Lance; Dunbar, David C.
- Nuclear Physics B, Vol. 435, Issue 1-2
Multi-loop Integrand Reduction with Computational Algebraic Geometry
journal, June 2014
- Badger, Simon; Frellesvig, Hjalte; Zhang, Yang
- Journal of Physics: Conference Series, Vol. 523
Space-time S-matrix and flux tube S-matrix II. Extracting and matching data
journal, January 2014
- Basso, Benjamin; Sever, Amit; Vieira, Pedro
- Journal of High Energy Physics, Vol. 2014, Issue 1
Dual superconformal invariance, momentum twistors and Grassmannians
journal, November 2009
- Mason, Lionel; Skinner, David
- Journal of High Energy Physics, Vol. 2009, Issue 11
Yangian symmetry of scattering amplitudes in 𝒩 = 4 super Yang-Mills theory
journal, May 2009
- Drummond, James; Henn, Johannes; Plefka, Jan
- Journal of High Energy Physics, Vol. 2009, Issue 05
Motivic amplitudes and cluster coordinates
journal, January 2014
- Golden, J. K.; Goncharov, A. B.; Spradlin, M.
- Journal of High Energy Physics, Vol. 2014, Issue 1
The differential of all two-loop MHV amplitudes in $ \mathcal{N}=4 $ Yang-Mills theory
journal, September 2013
- Golden, John; Spradlin, Marcus
- Journal of High Energy Physics, Vol. 2013, Issue 9
One-loop n-point gauge theory amplitudes, unitarity and collinear limits
journal, August 1994
- Bern, Zvi; Dixon, Lance; Dunbar, David C.
- Nuclear Physics B, Vol. 425, Issue 1-2
Dual-conformal regularization of infrared loop divergences and the chiral box expansion
journal, January 2015
- Bourjaily, Jacob; Caron-Huot, Simon; Trnka, Jaroslav
- Journal of High Energy Physics, Vol. 2015, Issue 1
The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM
journal, January 2011
- Arkani-Hamed, N.; Bourjaily, J.; Cachazo, F.
- Journal of High Energy Physics, Vol. 2011, Issue 1
A duality for the S matrix
journal, March 2010
- Arkani-Hamed, N.; Cachazo, F.; Cheung, C.
- Journal of High Energy Physics, Vol. 2010, Issue 3
OPE for all helicity amplitudes
journal, August 2015
- Basso, Benjamin; Caetano, João; Córdova, Lucía
- Journal of High Energy Physics, Vol. 2015, Issue 8
Space-time S-matrix and flux-tube S-matrix IV. Gluons and fusion
journal, September 2014
- Basso, Benjamin; Sever, Amit; Vieira, Pedro
- Journal of High Energy Physics, Vol. 2014, Issue 9
Multi-loop integrand reduction techniques
conference, August 2014
- Badger, Simon; Frellesvig, Hjalte Axel; Zhang, Yang
- Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2014)
Uniqueness of two-loop master contours
journal, October 2012
- Caron-Huot, Simon; Larsen, Kasper J.
- Journal of High Energy Physics, Vol. 2012, Issue 10
All tree-level amplitudes in 𝒩 = 4 SYM
journal, April 2009
- Drummond, J. M.; Henn, J. M.
- Journal of High Energy Physics, Vol. 2009, Issue 04
The Grassmannian origin of dual superconformal invariance
journal, March 2010
- Arkani-Hamed, Nima; Cachazo, Freddy; Cheung, Clifford
- Journal of High Energy Physics, Vol. 2010, Issue 3
Local integrals for planar scattering amplitudes
journal, June 2012
- Arkani-Hamed, N.; Bourjaily, J.; Cachazo, F.
- Journal of High Energy Physics, Vol. 2012, Issue 6
The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory
journal, June 2014
- Dixon, Lance J.; Drummond, James M.; Duhr, Claude
- Journal of High Energy Physics, Vol. 2014, Issue 6
Motivic amplitudes and cluster coordinates
text, January 2014
- Golden, J. K.; Goncharov, Alexander B.; Spradlin, Marcus
- ETH Zurich
What is the Simplest Quantum Field Theory?
text, January 2008
- Arkani-Hamed, Nima; Cachazo, Freddy; Kaplan, Jared
- arXiv
Eliminating spurious poles from gauge-theoretic amplitudes
preprint, January 2009
- Hodges, Andrew
- arXiv
Dual Superconformal Invariance, Momentum Twistors and Grassmannians
text, January 2009
- Mason, Lionel; Skinner, David
- arXiv
Bootstrapping the three-loop hexagon
text, January 2011
- Dixon, Lance J.; Drummond, James M.; Henn, Johannes M.
- arXiv
Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
text, January 2011
- Dixon, Lance J.; Drummond, James M.; Henn, Johannes M.
- arXiv
Uniqueness of two-loop master contours
text, January 2012
- Caron-Huot, Simon; Larsen, Kasper J.
- arXiv
Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods
text, January 2012
- Zhang, Yang
- arXiv
Multiloop integrals in dimensional regularization made simple
text, January 2013
- Henn, Johannes M.
- arXiv
Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
text, January 2013
- Basso, Benjamin; Sever, Amit; Vieira, Pedro
- arXiv
Analytic results for two-loop master integrals for Bhabha scattering I
text, January 2013
- Henn, Johannes M.; Smirnov, Vladimir A.
- arXiv
The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
text, January 2014
- Dixon, Lance J.; Drummond, James M.; Duhr, Claude
- arXiv
Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions
text, January 2014
- Henn, Johannes M.; Melnikov, Kirill; Smirnov, Vladimir A.
- arXiv
Bootstrapping six-gluon scattering in planar ${\cal N}=4$ super-Yang-Mills theory
preprint, January 2014
- Dixon, Lance J.; Drummond, James M.; Duhr, Claude
- arXiv
Bootstrapping an NMHV amplitude through three loops
text, January 2014
- Dixon, Lance J.; von Hippel, Matt
- arXiv
OPE for all Helicity Amplitudes
text, January 2014
- Basso, Benjamin; Caetano, Joao; Cordova, Lucia
- arXiv
One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
text, January 1994
- Bern, Z.; Dixon, L.; Dunbar, D. C.
- arXiv
Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
text, January 1994
- Bern, Z.; Dixon, L.; Dunbar, D. C.
- arXiv
New Recursion Relations for Tree Amplitudes of Gluons
text, January 2004
- Britto, Ruth; Cachazo, Freddy; Feng, Bo
- arXiv
Works referencing / citing this record:
All-Multiplicity Nonplanar Amplitude Integrands in Maximally Supersymmetric Yang-Mills Theory at Two Loops
journal, March 2020
- Bourjaily, Jacob L.; Herrmann, Enrico; Langer, Cameron
- Physical Review Letters, Vol. 124, Issue 11
Two-loop $$ \mathcal{N} $$ = 2 SQCD amplitudes with external matter from iterated cuts
journal, July 2019
- Kälin, Gregor; Mogull, Gustav; Ochirov, Alexander
- Journal of High Energy Physics, Vol. 2019, Issue 7
Positivity, Grassmannian geometry and simplex-like structures of scattering amplitudes
journal, December 2017
- Rao, Junjie
- Journal of High Energy Physics, Vol. 2017, Issue 12
The cosmic Galois group and extended Steinmann relations for planar N $$ \mathcal{N} $$ = 4 SYM amplitudes
text, January 2019
- Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes
text, January 2019
- Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory
text, January 2015
- Badger, Simon; Mogull, Gustav; Ochirov, Alexander
- arXiv
Evidence for a Nonplanar Amplituhedron
text, January 2015
- Bern, Zvi; Herrmann, Enrico; Litsey, Sean
- arXiv
Prescriptive Unitarity
text, January 2017
- Bourjaily, Jacob L.; Herrmann, Enrico; Trnka, Jaroslav
- arXiv
Rationalizing Loop Integration
text, January 2018
- Bourjaily, Jacob L.; McLeod, Andrew J.; von Hippel, Matt
- arXiv
Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function
text, January 2018
- Golden, John; McLeod, Andrew J.
- arXiv
Two-loop $\mathcal{N}=2$ SQCD amplitudes with external matter from iterated cuts
text, January 2018
- Kälin, Gregor; Mogull, Gustav; Ochirov, Alexander
- arXiv
The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes
text, January 2019
- Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko
- arXiv
Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
text, January 2019
- Bourjaily, Jacob L.; Herrmann, Enrico; Langer, Cameron
- arXiv