Evidence for a nonplanar amplituhedron

J. Drummond, J. Henn, V. Smirnov and E. Sokatchev, Magic identities for conformal four-point integrals, JHEP 01 (2007) 064 [ hep-th/0607160 ].

L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [ arXiv:0705.0303 ] [ INSPIRE ].

J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Dual superconformal symmetry of scattering amplitudes in N = 4 super-Yang-Mills theory, Nucl. Phys. B 828 (2010) 317 [ arXiv:0807.1095 ] [ INSPIRE ].

J.M. Drummond, J.M. Henn and J. Plefka, Yangian symmetry of scattering amplitudes in N = 4 super Yang-Mills theory, JHEP 05 (2009) 046 [ arXiv:0902.2987 ] [ INSPIRE ].

N. Beisert and M. Staudacher, The N = 4 SYM integrable super spin chain, Nucl. Phys. B 670 (2003) 439 [ hep-th/0307042 ] [ INSPIRE ].

N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech. 0701 (2007) P01021 [ hep-th/0610251 ] [ INSPIRE ].

J.M. Drummond, G.P. Korchemsky and E. Sokatchev, Conformal properties of four-gluon planar amplitudes and Wilson loops, Nucl. Phys. B 795 (2008) 385 [ arXiv:0707.0243 ] [ INSPIRE ].

A. Brandhuber, P. Heslop and G. Travaglini, MHV amplitudes in N = 4 super Yang-Mills and Wilson loops, Nucl. Phys. B 794 (2008) 231 [ arXiv:0707.1153 ] [ INSPIRE ].

J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes, Nucl. Phys. B 826 (2010) 337 [ arXiv:0712.1223 ] [ INSPIRE ].

L.J. Mason and D. Skinner, The complete planar S-matrix of N = 4 SYM as a Wilson loop in twistor space, JHEP 12 (2010) 018 [ arXiv:1009.2225 ] [ INSPIRE ].

S. Caron-Huot, Notes on the scattering amplitude/Wilson loop duality, JHEP 07 (2011) 058 [ arXiv:1010.1167 ] [ INSPIRE ].

L.F. Alday, B. Eden, G.P. Korchemsky, J. Maldacena and E. Sokatchev, From correlation functions to Wilson loops, JHEP 09 (2011) 123 [ arXiv:1007.3243 ] [ INSPIRE ].

B. Basso, A. Sever and P. Vieira, Spacetime and flux tube S-matrices at finite coupling for N =4 supersymmetric Yang-Mills theory, Phys. Rev. Lett. 111 (2013) 091602 [ arXiv:1303.1396 ] [ INSPIRE ].

B. Basso, J. Caetano, L. Cordova, A. Sever and P. Vieira, OPE for all helicity amplitudes, JHEP 08 (2015) 018 [ arXiv:1412.1132 ] [ INSPIRE ].

B. Basso, A. Sever and P. Vieira, Hexagonal Wilson loops in planar N $$ \mathcal{N} $$ = 4 SYM theory at finite coupling, arXiv:1508.0304 .

L.J. Dixon, J.M. Drummond and J.M. Henn, Bootstrapping the three-loop hexagon, JHEP 11 (2011) 023 [ arXiv:1108.4461 ] [ INSPIRE ].

L.J. Dixon, J.M. Drummond and J.M. Henn, Analytic result for the two-loop six-point NMHV amplitude in N = 4 super Yang-Mills theory, JHEP 01 (2012) 024 [ arXiv:1111.1704 ] [ INSPIRE ].

L.J. Dixon, J.M. Drummond, M. von Hippel and J. Pennington, Hexagon functions and the three-loop remainder function, JHEP 12 (2013) 049 [ arXiv:1308.2276 ] [ INSPIRE ].

L.J. Dixon and M. von Hippel, Bootstrapping an NMHV amplitude through three loops, JHEP 10 (2014) 065 [ arXiv:1408.1505 ] [ INSPIRE ].

L.J. Dixon, M. von Hippel and A.J. McLeod, The four-loop six-gluon NMHV ratio function, arXiv:1509.0812 .

A.B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, Classical polylogarithms for amplitudes and Wilson loops, Phys. Rev. Lett. 105 (2010) 151605 [ arXiv:1006.5703 ] [ INSPIRE ].

J. Golden, A.B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, Motivic amplitudes and cluster coordinates, JHEP 01 (2014) 091 [ arXiv:1305.1617 ] [ INSPIRE ].

J.M. Drummond, G. Papathanasiou and M. Spradlin, A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon, JHEP 03 (2015) 072 [ arXiv:1412.3763 ] [ INSPIRE ].

D. Parker, A. Scherlis, M. Spradlin and A. Volovich, Hedgehog bases for A n cluster polylogarithms and an application to six-point amplitudes, JHEP 11 (2015) 136 [ arXiv:1507.0195 ].

N. Arkani-Hamedet al., Scattering amplitudes and the positive grassmannian, arXiv:1212.5605 .

N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, A duality for the S matrix, JHEP 03 (2010) 020 [ arXiv:0907.5418 ] [ INSPIRE ].

N. Arkani-Hamed, F. Cachazo and C. Cheung, The grassmannian origin of dual superconformal invariance, JHEP 03 (2010) 036 [ arXiv:0909.0483 ] [ INSPIRE ].

L.J. Mason and D. Skinner, Dual superconformal invariance, momentum twistors and grassmannians, JHEP 11 (2009) 045 [ arXiv:0909.0250 ] [ INSPIRE ].

N. Arkani-Hamed, J. Bourjaily, F. Cachazo and J. Trnka, Unification of residues and grassmannian dualities, JHEP 01 (2011) 049 [ arXiv:0912.4912 ] [ INSPIRE ].

N. Arkani-Hamed, J. Bourjaily, F. Cachazo and J. Trnka, Local spacetime physics from the grassmannian, JHEP 01 (2011) 108 [ arXiv:0912.3249 ] [ INSPIRE ].

N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, S. Caron-Huot and J. Trnka, The all-loop integrand for scattering amplitudes in planar N = 4 SYM, JHEP 01 (2011) 041 [ arXiv:1008.2958 ] [ INSPIRE ].

Y.-T. Huang and C. Wen, ABJM amplitudes and the positive orthogonal grassmannian, JHEP 02 (2014) 104 [ arXiv:1309.3252 ] [ INSPIRE ].

Y.-t. Huang, C. Wen and D. Xie, The positive orthogonal grassmannian and loop amplitudes of ABJM, J. Phys. A 47 (2014) 474008 [ arXiv:1402.1479 ] [ INSPIRE ].

J. Kim and S. Lee, Positroid stratification of orthogonal grassmannian and ABJM amplitudes, JHEP 09 (2014) 085 [ arXiv:1402.1119 ] [ INSPIRE ].

H. Elvang et al., Grassmannians for scattering amplitudes in 4D N $$ \mathcal{N} $$ = 4 SYM and 3D ABJM, JHEP 12 (2014) 181 [ arXiv:1410.0621 ] [ INSPIRE ].

N. Arkani-Hamed and J. Trnka, The amplituhedron, JHEP 10 (2014) 030 [ arXiv:1312.2007 ] [ INSPIRE ].

N. Arkani-Hamed and J. Trnka, Into the amplituhedron, JHEP 12 (2014) 182 [ arXiv:1312.7878 ] [ INSPIRE ].

S. Franco, D. Galloni, A. Mariotti and J. Trnka, Anatomy of the amplituhedron, JHEP 03 (2015) 128 [ arXiv:1408.3410 ] [ INSPIRE ].

Y. Bai and S. He, The amplituhedron from momentum twistor diagrams, JHEP 02 (2015) 065 [ arXiv:1408.2459 ] [ INSPIRE ].

N. Arkani-Hamed, A. Hodges and J. Trnka, Positive amplitudes in the amplituhedron, JHEP 08 (2015) 030 [ arXiv:1412.8478 ] [ INSPIRE ].

T. Lam, Amplituhedron cells and Stanley symmetric functions, Commun. Math. Phys. 343 (2016) 1025 [ arXiv:1408.5531 ] [ INSPIRE ].

Y. Bai, S. He and T. Lam, The amplituhedron and the one-loop Grassmannian measure, arXiv:1510.0355 .

L. Ferro, T. Lukowski, A. Orta and M. Parisi, Towards the amplituhedron volume, arXiv:1512.0495 .

G. Lusztig, Total positivity in partial flag manifolds, Represent. Theory 2 (1998) 70.

A. Postnikov, Total positivity, Grassmannians and networks, math/0609764 [ INSPIRE ].

A. Postnikov, D. Speyer and L. Williams, Matching polytopes, toric geometry, and the non-negative part of the Grassmannian, arXiv:0706.2501 .

L.K. Williams, Enumeration of totally positive Grassmann cells, math/0307271 .

A.B. Goncharov and R. Kenyon, Dimers and cluster integrable systems, arXiv:1107.5588 [ INSPIRE ].

A. Knutson, T. Lam and D. Speyer, Positroid varieties: juggling and geometry, arXiv:1111.3660 .

Z. Bern, J.J.M. Carrasco and H. Johansson, New relations for gauge-theory amplitudes, Phys. Rev. D 78 (2008) 085011 [ arXiv:0805.3993 ] [ INSPIRE ].

Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative quantum gravity as a double copy of gauge theory, Phys. Rev. Lett. 105 (2010) 061602 [ arXiv:1004.0476 ] [ INSPIRE ].

N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo and J. Trnka, Singularity structure of maximally supersymmetric scattering amplitudes, Phys. Rev. Lett. 113 (2014) 261603 [ arXiv:1410.0354 ] [ INSPIRE ].

Z. Bern, E. Herrmann, S. Litsey, J. Stankowicz and J. Trnka, Logarithmic singularities and maximally supersymmetric amplitudes, JHEP 06 (2015) 202 [ arXiv:1412.8584 ] [ INSPIRE ].

S.J. Parke and T.R. Taylor, An amplitude for n gluon scattering, Phys. Rev. Lett. 56 (1986) 2459 [ INSPIRE ].

M.L. Mangano, S.J. Parke and Z. Xu, Duality and multi-gluon scattering, Nucl. Phys. B 298 (1988) 653 [ INSPIRE ].

N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, A. Postnikov and J. Trnka, On-shell structures of MHV amplitudes beyond the planar limit, JHEP 06 (2015) 179 [ arXiv:1412.8475 ] [ INSPIRE ].

L.J. Dixon, A.J. McLeod, J. Trnka and M. von Hippel, to appear.

Z. Bern et al., Three-Loop Superfiniteness of N = 8 Supergravity, Phys. Rev. Lett. 98 (2007) 161303 [ hep-th/0702112 ] [ INSPIRE ].

J.J. Carrasco and H. Johansson, Five-point amplitudes in N = 4 super-Yang-Mills theory and N = 8 supergravity, Phys. Rev. D 85 (2012) 025006 [ arXiv:1106.4711 ] [ INSPIRE ].

Z. Bern, J.J. Carrasco, T. Dennen, Y.-t. Huang and H. Ita, Generalized unitarity and six-dimensional helicity, Phys. Rev. D 83 (2011) 085022 [ arXiv:1010.0494 ] [ INSPIRE ].

Z. Bern et al., The two-loop six-gluon MHV amplitude in maximally supersymmetric Yang-Mills theory, Phys. Rev. D 78 (2008) 045007 [ arXiv:0803.1465 ] [ INSPIRE ].

Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [ hep-ph/9403226 ] [ INSPIRE ].

Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys. B 435 (1995) 59 [ hep-ph/9409265 ] [ INSPIRE ].

Z. Bern, J.J.M. Carrasco, H. Johansson and D.A. Kosower, Maximally supersymmetric planar Yang-Mills amplitudes at five loops, Phys. Rev. D 76 (2007) 125020 [ arXiv:0705.1864 ] [ INSPIRE ].

R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [ hep-th/0501052 ] [ INSPIRE ].

A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, JHEP 05 (2013) 135 [ arXiv:0905.1473 ] [ INSPIRE ].

F. Cachazo, Sharpening the leading singularity, arXiv:0803.1988 [ INSPIRE ].

J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude, Phys. Lett. B 662 (2008) 456 [ arXiv:0712.4138 ] [ INSPIRE ].

N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo and J. Trnka, Local integrals for planar scattering amplitudes, JHEP 06 (2012) 125 [ arXiv:1012.6032 ] [ INSPIRE ].

E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [ hep-th/0312171 ] [ INSPIRE ].

J.L. Bourjaily, S. Caron-Huot and J. Trnka, Dual-conformal regularization of infrared loop divergences and the chiral box expansion, JHEP 01 (2015) 001 [ arXiv:1303.4734 ] [ INSPIRE ].

J.L. Bourjaily and J. Trnka, Local integrand representations of all two-loop amplitudes in planar SYM, JHEP 08 (2015) 119 [ arXiv:1505.0588 ].

Z. Bern, J.S. Rozowsky and B. Yan, Two loop four gluon amplitudes in N = 4 super Yang-Mills, Phys. Lett. B 401 (1997) 273 [ hep-ph/9702424 ] [ INSPIRE ].

R. Kleiss and H. Kuijf, Multi-gluon cross-sections and five jet production at hadron colliders, Nucl. Phys. B 312 (1989) 616 [ INSPIRE ].

Z. Bern, L.J. Dixon, D.C. Dunbar, M. Perelstein and J.S. Rozowsky, On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences, Nucl. Phys. B 530 (1998) 401 [ hep-th/9802162 ] [ INSPIRE ].

Z. Bern, J.J.M. Carrasco, L.J. Dixon, H. Johansson and R. Roiban, Simplifying multiloop integrands and ultraviolet divergences of gauge theory and gravity amplitudes, Phys. Rev. D 85 (2012) 105014 [ arXiv:1201.5366 ] [ INSPIRE ].

M.L. Mangano and S.J. Parke, Multiparton amplitudes in gauge theories, Phys. Rept. 200 (1991) 301 [ hep-th/0509223 ] [ INSPIRE ].

S. Franco, D. Galloni, B. Penante, and C. Wen, Non-planar on-shell diagrams, JHEP 06 (2015) 199 [ arXiv:1502.0203 ].

Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop selfdual and N = 4 super Yang-Mills, Phys. Lett. B 394 (1997) 105 [ hep-th/9611127 ] [ INSPIRE ].

Z. Bern, L.J. Dixon, M. Perelstein and J.S. Rozowsky, Multileg one loop gravity amplitudes from gauge theory, Nucl. Phys. B 546 (1999) 423 [ hep-th/9811140 ] [ INSPIRE ].

G. Mogull and D. O’Connell, Overcoming obstacles to colour-kinematics duality at two loops, arXiv:1511.0665 .

A.V. Kotikov, L.N. Lipatov, A.I. Onishchenko and V.N. Velizhanin, Three loop universal anomalous dimension of the Wilson operators in N = 4 SUSY Yang-Mills model, Phys. Lett. B 595 (2004) 521 [Erratum ibid. B 632 (2006) 754] [ hep-th/0404092 ] [ INSPIRE ].

J.M. Henn, Multiloop integrals in dimensional regularization made simple, Phys. Rev. Lett. 110 (2013) 251601 [ arXiv:1304.1806 ] [ INSPIRE ].

J.M. Henn, A.V. Smirnov and V.A. Smirnov, Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation, JHEP 07 (2013) 128 [ arXiv:1306.2799 ] [ INSPIRE ].

S. Caron-Huot and J.M. Henn, Iterative structure of finite loop integrals, JHEP 06 (2014) 114 [ arXiv:1404.2922 ] [ INSPIRE ].

J.M. Henn, Lectures on differential equations for Feynman integrals, J. Phys. A 48 (2015) 153001 [ arXiv:1412.2296 ] [ INSPIRE ].

T. Gehrmann, J.M. Henn and N.A. Lo Presti, Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD, arXiv:1511.0540 .