Abstract
In this paper, we present new expressions for n-point NMHV tree-level gravity amplitudes. We introduce a method of factorization diagrams which is a simple graphical representation of R-invariants in Yang-Mills theory. We define the gravity analogues which we call \( \mathcal{G} \)-invariants, and expand the NMHV gravity amplitudes in terms of these objects. We provide explicit formulas of NMHV gravity amplitudes up to eight points in terms of \( \mathcal{G} \)-invariants, and give the general definition for any number of points. We discuss the connection to BCFW representation, special behavior under large momentum shift, the role of momentum twistors and the intricate web of spurious poles cancelation. Because of the close connection between R-invariants and the (tree-level) Amplituhedron for Yang-Mills amplitudes, we speculate that the new expansion for gravity amplitudes should correspond to the triangulation of the putative Gravituhedron geometry.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Arkani-Hamed and J. Trnka, The amplituhedron, JHEP 10 (2014) 030 [arXiv:1312.2007] [INSPIRE].
N. Arkani-Hamed, Y. Bai and T. Lam, Positive geometries and canonical forms, JHEP 11 (2017) 039 [arXiv:1703.04541] [INSPIRE].
N. Arkani-Hamed, H. Thomas and J. Trnka, Unwinding the amplituhedron in binary, JHEP 01 (2018) 016 [arXiv:1704.05069] [INSPIRE].
A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, JHEP 05 (2013) 135 [arXiv:0905.1473] [INSPIRE].
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, A. Hodges and J. Trnka, A note on polytopes for scattering amplitudes, JHEP 04 (2012) 081 [arXiv:1012.6030] [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].
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, Local spacetime physics from the grassmannian, JHEP 01 (2011) 108 [arXiv:0912.3249] [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. L. Bourjaily, F. Cachazo, A. B. Goncharov, A. Postnikov and J. Trnka, Grassmannian geometry of scattering amplitudes, Cambridge University Press, Cambridge, U.K. (2016) [arXiv:1212.5605] [INSPIRE].
S. Franco, D. Galloni, A. Mariotti and J. Trnka, Anatomy of the amplituhedron, JHEP 03 (2015) 128 [arXiv:1408.3410] [INSPIRE].
T. Lukowski, On the boundaries of the m = 2 amplituhedron, arXiv:1908.00386 [INSPIRE].
T. Łukowski and R. Moerman, Boundaries of the amplituhedron with amplituhedronBoundaries, Comput. Phys. Commun. 259 (2021) 107653 [arXiv:2002.07146] [INSPIRE].
L. Ferro, T. Łukowski and R. Moerman, From momentum amplituhedron boundaries to amplitude singularities and back, JHEP 07 (2020) 201 [arXiv:2003.13704] [INSPIRE].
I. Prlina, M. Spradlin, J. Stankowicz and S. Stanojevic, Boundaries of amplituhedra and NMHV symbol alphabets at two loops, JHEP 04 (2018) 049 [arXiv:1712.08049] [INSPIRE].
T. Dennen, I. Prlina, M. Spradlin, S. Stanojevic and A. Volovich, Landau singularities from the amplituhedron, JHEP 06 (2017) 152 [arXiv:1612.02708] [INSPIRE].
D. Galloni, Positivity sectors and the amplituhedron, arXiv:1601.02639 [INSPIRE].
R. Kojima and C. Langer, Sign flip triangulations of the amplituhedron, JHEP 05 (2020) 121 [arXiv:2001.06473] [INSPIRE].
R. Kojima and J. Rao, Triangulation-free trivialization of 2-loop MHV amplituhedron, JHEP 10 (2020) 140 [arXiv:2007.15650] [INSPIRE].
L. Ferro, T. Łukowski, A. Orta and M. Parisi, Yangian symmetry for the tree amplituhedron, J. Phys. A 50 (2017) 294005 [arXiv:1612.04378] [INSPIRE].
L. Ferro, T. Lukowski, A. Orta and M. Parisi, Tree-level scattering amplitudes from the amplituhedron, J. Phys. Conf. Ser. 841 (2017) 012037 [arXiv:1612.06276] [INSPIRE].
T. Lam, Amplituhedron cells and Stanley symmetric functions, Commun. Math. Phys. 343 (2016) 1025 [arXiv:1408.5531] [INSPIRE].
S. N. Karp and L. K. Williams, The m = 1 amplituhedron and cyclic hyperplane arrangements, Int. Math. Res. Not. 5 (2019) 1401 [arXiv:1608.08288] [INSPIRE].
S. N. Karp, L. K. Williams and Y. X. Zhang, Decompositions of amplituhedra, arXiv:1708.09525 [INSPIRE].
P. Galashin and T. Lam, Parity duality for the amplituhedron, Compos. Math. 156 (2020) 2207 [arXiv:1805.00600] [INSPIRE].
T. Lukowski, M. Parisi and L. K. Williams, The positive tropical grassmannian, the hypersimplex, and the m = 2 amplituhedron, arXiv:2002.06164 [INSPIRE].
F. Mohammadi, L. Monin and M. Parisi, Triangulations and canonical forms of amplituhedra: a fiber-based approach beyond polytopes, arXiv:2010.07254 [INSPIRE].
N. Arkani-Hamed, C. Langer, A. Yelleshpur Srikant and J. Trnka, Deep into the amplituhedron: amplitude singularities at all loops and legs, Phys. Rev. Lett. 122 (2019) 051601 [arXiv:1810.08208] [INSPIRE].
C. Langer and A. Yelleshpur Srikant, All-loop cuts from the amplituhedron, JHEP 04 (2019) 105 [arXiv:1902.05951] [INSPIRE].
Y. An, Y. Li, Z. Li and J. Rao, All-loop Mondrian diagrammatics and 4-particle amplituhedron, JHEP 06 (2018) 023 [arXiv:1712.09994] [INSPIRE].
N. Arkani-Hamed, A. Hodges and J. Trnka, Positive amplitudes in the amplituhedron, JHEP 08 (2015) 030 [arXiv:1412.8478] [INSPIRE].
L. Ferro, T. Lukowski, A. Orta and M. Parisi, Towards the amplituhedron volume, JHEP 03 (2016) 014 [arXiv:1512.04954] [INSPIRE].
E. Herrmann, C. Langer, J. Trnka and M. Zheng, Positive geometry, local triangulations, and the dual of the amplituhedron, JHEP 01 (2021) 035 [arXiv:2009.05607] [INSPIRE].
N. Arkani-Hamed, Y. Bai, S. He and G. Yan, Scattering forms and the positive geometry of kinematics, color and the worldsheet, JHEP 05 (2018) 096 [arXiv:1711.09102] [INSPIRE].
S. He, G. Yan, C. Zhang and Y. Zhang, Scattering forms, worldsheet forms and amplitudes from subspaces, JHEP 08 (2018) 040 [arXiv:1803.11302] [INSPIRE].
L. de la Cruz, A. Kniss and S. Weinzierl, Properties of scattering forms and their relation to associahedra, JHEP 03 (2018) 064 [arXiv:1711.07942] [INSPIRE].
H. Frost, Biadjoint scalar tree amplitudes and intersecting dual associahedra, JHEP 06 (2018) 153 [arXiv:1802.03384] [INSPIRE].
V. Bazier-Matte, G. Douville, K. Mousavand, H. Thomas and E. Yıldırım, ABHY associahedra and Newton polytopes of F -polynomials for finite type cluster algebras, arXiv:1808.09986 [INSPIRE].
G. Salvatori, 1-loop amplitudes from the halohedron, JHEP 12 (2019) 074 [arXiv:1806.01842] [INSPIRE].
N. Arkani-Hamed, S. He, G. Salvatori and H. Thomas, Causal diamonds, cluster polytopes and scattering amplitudes, arXiv:1912.12948 [INSPIRE].
P. Banerjee, A. Laddha and P. Raman, Stokes polytopes: the positive geometry for ϕ4 interactions, JHEP 08 (2019) 067 [arXiv:1811.05904] [INSPIRE].
P. B. Aneesh, P. Banerjee, M. Jagadale, R. Rajan, A. Laddha and S. Mahato, On positive geometries of quartic interactions: Stokes polytopes, lower forms on associahedra and world-sheet forms, JHEP 04 (2020) 149 [arXiv:1911.06008] [INSPIRE].
M. Jagadale and A. Laddha, On the positive geometry of quartic interactions III: one loop integrands from polytopes, arXiv:2007.12145 [INSPIRE].
R. R. John, R. Kojima and S. Mahato, Weights, recursion relations and projective triangulations for positive geometry of scalar theories, JHEP 10 (2020) 037 [arXiv:2007.10974] [INSPIRE].
R. Kojima, Weights and recursion relations for ϕp tree amplitudes from the positive geometry, JHEP 08 (2020) 054 [arXiv:2005.11006] [INSPIRE].
N. Kalyanapuram and R. G. Jha, Positive geometries for all scalar theories from twisted intersection theory, Phys. Rev. Res. 2 (2020) 033119 [arXiv:2006.15359] [INSPIRE].
P. B. Aneesh, M. Jagadale and N. Kalyanapuram, Accordiohedra as positive geometries for generic scalar field theories, Phys. Rev. D 100 (2019) 106013 [arXiv:1906.12148] [INSPIRE].
A. Herderschee, S. He, F. Teng and Y. Zhang, On positive geometry and scattering forms for matter particles, JHEP 06 (2020) 030 [arXiv:1912.08307] [INSPIRE].
E. Herrmann, C. Langer, J. Trnka and M. Zheng, Positive geometries for one-loop chiral octagons, arXiv:2007.12191 [INSPIRE].
N. Arkani-Hamed, S. He and T. Lam, Stringy canonical forms, JHEP 02 (2021) 069 [arXiv:1912.08707] [INSPIRE].
Y.-T. Huang, J.-Y. Liu, L. Rodina and Y. Wang, Carving out the space of open-string S-matrix, arXiv:2008.02293 [INSPIRE].
S. He, Z. Li, P. Raman and C. Zhang, Stringy canonical forms and binary geometries from associahedra, cyclohedra and generalized permutohedra, JHEP 10 (2020) 054 [arXiv:2005.07395] [INSPIRE].
S. He, L. Ren and Y. Zhang, Notes on polytopes, amplitudes and boundary configurations for Grassmannian string integrals, JHEP 04 (2020) 140 [arXiv:2001.09603] [INSPIRE].
A. Herderschee and F. Teng, Open associahedra and scattering forms, JHEP 12 (2020) 134 [arXiv:2008.06418] [INSPIRE].
N. Arkani-Hamed, P. Benincasa and A. Postnikov, Cosmological polytopes and the wavefunction of the universe, arXiv:1709.02813 [INSPIRE].
P. Benincasa, Cosmological polytopes and the wavefuncton of the universe for light states, arXiv:1909.02517 [INSPIRE].
N. Arkani-Hamed, Y.-T. Huang and S.-H. Shao, On the positive geometry of conformal field theory, JHEP 06 (2019) 124 [arXiv:1812.07739] [INSPIRE].
S. He and C. Zhang, Notes on scattering amplitudes as differential forms, JHEP 10 (2018) 054 [arXiv:1807.11051] [INSPIRE].
S. He and Q. Yang, An etude on recursion relations and triangulations, JHEP 05 (2019) 040 [arXiv:1810.08508] [INSPIRE].
D. Damgaard, L. Ferro, T. Lukowski and M. Parisi, The momentum amplituhedron, JHEP 08 (2019) 042 [arXiv:1905.04216] [INSPIRE].
D. Damgaard, L. Ferro, T. Lukowski and R. Moerman, Momentum amplituhedron meets kinematic associahedron, JHEP 02 (2021) 041 [arXiv:2010.15858] [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].
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].
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].
Z. Bern, E. Herrmann, S. Litsey, J. Stankowicz and J. Trnka, Evidence for a nonplanar amplituhedron, JHEP 06 (2016) 098 [arXiv:1512.08591] [INSPIRE].
J. L. Bourjaily, S. Franco, D. Galloni and C. Wen, Stratifying on-shell cluster varieties: the geometry of non-planar on-shell diagrams, JHEP 10 (2016) 003 [arXiv:1607.01781] [INSPIRE].
J. L. Bourjaily, E. Herrmann and J. Trnka, Maximally supersymmetric amplitudes at infinite loop momentum, Phys. Rev. D 99 (2019) 066006 [arXiv:1812.11185] [INSPIRE].
J. L. Bourjaily, E. Herrmann, C. Langer, A. J. McLeod and J. Trnka, Prescriptive unitarity for non-planar six-particle amplitudes at two loops, JHEP 12 (2019) 073 [arXiv:1909.09131] [INSPIRE].
J. L. Bourjaily, E. Herrmann, C. Langer, A. J. McLeod and J. Trnka, All-multiplicity nonplanar amplitude integrands in maximally supersymmetric Yang-Mills theory at two loops, Phys. Rev. Lett. 124 (2020) 111603 [arXiv:1911.09106] [INSPIRE].
Z. Bern, M. Enciso, C.-H. Shen and M. Zeng, Dual conformal structure beyond the planar limit, Phys. Rev. Lett. 121 (2018) 121603 [arXiv:1806.06509] [INSPIRE].
Z. Bern, M. Enciso, H. Ita and M. Zeng, Dual conformal symmetry, integration-by-parts reduction, differential equations and the nonplanar sector, Phys. Rev. D 96 (2017) 096017 [arXiv:1709.06055] [INSPIRE].
H. Kawai, D. C. Lewellen and S. H. H. Tye, A relation between tree amplitudes of closed and open strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].
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].
Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson and R. Roiban, The duality between color and kinematics and its applications, arXiv:1909.01358 [INSPIRE].
F. Cachazo, S. He and E. Y. Yuan, Scattering of massless particles: scalars, gluons and gravitons, JHEP 07 (2014) 033 [arXiv:1309.0885] [INSPIRE].
F. Cachazo, S. He and E. Y. Yuan, Scattering of massless particles in arbitrary dimensions, Phys. Rev. Lett. 113 (2014) 171601 [arXiv:1307.2199] [INSPIRE].
F. Cachazo, S. He and E. Y. Yuan, Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM, JHEP 07 (2015) 149 [arXiv:1412.3479] [INSPIRE].
E. Casali and A. Sharma, Celestial double copy from the worldsheet, arXiv:2011.10052 [INSPIRE].
E. Casali and A. Puhm, Double copy for celestial amplitudes, Phys. Rev. Lett. 126 (2021) 101602 [arXiv:2007.15027] [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].
Z. Bern, J. J. Carrasco, W.-M. Chen, H. Johansson and R. Roiban, Gravity amplitudes as generalized double copies of gauge-theory amplitudes, Phys. Rev. Lett. 118 (2017) 181602 [arXiv:1701.02519] [INSPIRE].
Z. Bern et al., Ultraviolet properties of N = 8 supergravity at five loops, Phys. Rev. D 98 (2018) 086021 [arXiv:1804.09311] [INSPIRE].
R. Monteiro, D. O’Connell and C. D. White, Black holes and the double copy, JHEP 12 (2014) 056 [arXiv:1410.0239] [INSPIRE].
A. Luna et al., Perturbative spacetimes from Yang-Mills theory, JHEP 04 (2017) 069 [arXiv:1611.07508] [INSPIRE].
D. A. Kosower, B. Maybee and D. O’Connell, Amplitudes, observables, and classical scattering, JHEP 02 (2019) 137 [arXiv:1811.10950] [INSPIRE].
Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon and M. Zeng, Black hole binary dynamics from the double copy and effective theory, JHEP 10 (2019) 206 [arXiv:1908.01493] [INSPIRE].
Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon and M. Zeng, Scattering amplitudes and the conservative hamiltonian for binary systems at third post-minkowskian order, Phys. Rev. Lett. 122 (2019) 201603 [arXiv:1901.04424] [INSPIRE].
Z. Bern, J. Parra-Martinez, R. Roiban, E. Sawyer and C.-H. Shen, Leading nonlinear tidal effects and scattering amplitudes, arXiv:2010.08559 [INSPIRE].
R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308] [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].
F. Cachazo and P. Svrček, Tree level recursion relations in general relativity, hep-th/0502160 [INSPIRE].
J. Bedford, A. Brandhuber, B. J. Spence and G. Travaglini, A recursion relation for gravity amplitudes, Nucl. Phys. B 721 (2005) 98 [hep-th/0502146] [INSPIRE].
N. Arkani-Hamed and J. Kaplan, On tree amplitudes in gauge theory and gravity, JHEP 04 (2008) 076 [arXiv:0801.2385] [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].
E. Herrmann and J. Trnka, Gravity on-shell diagrams, JHEP 11 (2016) 136 [arXiv:1604.03479] [INSPIRE].
E. Herrmann and J. Trnka, UV cancellations in gravity loop integrands, JHEP 02 (2019) 084 [arXiv:1808.10446] [INSPIRE].
A. Edison, E. Herrmann, J. Parra-Martinez and J. Trnka, Gravity loop integrands from the ultraviolet, SciPost Phys. 10 (2021) 016 [arXiv:1909.02003] [INSPIRE].
J. Bjornsson and M. B. Green, 5 loops in 24/5 dimensions, JHEP 08 (2010) 132 [arXiv:1004.2692] [INSPIRE].
R. Kallosh and T. Kugo, The footprint of E7(7) amplitudes of N = 8 supergravity, JHEP 01 (2009) 072 [arXiv:0811.3414] [INSPIRE].
N. Beisert, H. Elvang, D. Z. Freedman, M. Kiermaier, A. Morales and S. Stieberger, E7(7) constraints on counterterms in N = 8 supergravity, Phys. Lett. B 694 (2011) 265 [arXiv:1009.1643] [INSPIRE].
Z. Bern, J. J. Carrasco, D. Forde, H. Ita and H. Johansson, Unexpected cancellations in gravity theories, Phys. Rev. D 77 (2008) 025010 [arXiv:0707.1035] [INSPIRE].
Z. Bern, M. Enciso, J. Parra-Martinez and M. Zeng, Manifesting enhanced cancellations in supergravity: integrands versus integrals, JHEP 05 (2017) 137 [arXiv:1703.08927] [INSPIRE].
Z. Bern, L. J. Dixon and R. Roiban, Is N = 8 supergravity ultraviolet finite?, Phys. Lett. B 644 (2007) 265 [hep-th/0611086] [INSPIRE].
S. J. Parke and T. R. Taylor, An amplitude for n gluon scattering, Phys. Rev. Lett. 56 (1986) 2459 [INSPIRE].
V. P. Nair, A current algebra for some gauge theory amplitudes, Phys. Lett. B 214 (1988) 215 [INSPIRE].
F. A. Berends, W. T. Giele and H. Kuijf, On relations between multi-gluon and multigraviton scattering, Phys. Lett. B 211 (1988) 91 [INSPIRE].
L. J. Mason and D. Skinner, Gravity, twistors and the MHV formalism, Commun. Math. Phys. 294 (2010) 827 [arXiv:0808.3907] [INSPIRE].
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516 [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].
D. Nguyen, M. Spradlin, A. Volovich and C. Wen, The tree formula for MHV graviton amplitudes, JHEP 07 (2010) 045 [arXiv:0907.2276] [INSPIRE].
A. Hodges, New expressions for gravitational scattering amplitudes, JHEP 07 (2013) 075 [arXiv:1108.2227] [INSPIRE].
P. Heslop and A. E. Lipstein, On-shell diagrams for N = 8 supergravity amplitudes, JHEP 06 (2016) 069 [arXiv:1604.03046] [INSPIRE].
J. A. Farrow and A. E. Lipstein, From 4d ambitwistor strings to on shell diagrams and back, JHEP 07 (2017) 114 [arXiv:1705.07087] [INSPIRE].
C. Armstrong, J. A. Farrow and A. E. Lipstein, N = 7 on-shell diagrams and supergravity amplitudes in momentum twistor space, JHEP 01 (2021) 181 [arXiv:2010.11813] [INSPIRE].
H. Elvang and D. Z. Freedman, Note on graviton MHV amplitudes, JHEP 05 (2008) 096 [arXiv:0710.1270] [INSPIRE].
J. M. Drummond, M. Spradlin, A. Volovich and C. Wen, Tree-level amplitudes in N = 8 supergravity, Phys. Rev. D 79 (2009) 105018 [arXiv:0901.2363] [INSPIRE].
A. Hodges, A simple formula for gravitational MHV amplitudes, arXiv:1204.1930 [INSPIRE].
F. Cachazo, L. Mason and D. Skinner, Gravity in twistor space and its grassmannian formulation, SIGMA 10 (2014) 051 [arXiv:1207.4712] [INSPIRE].
D. Skinner, Twistor strings for N = 8 supergravity, JHEP 04 (2020) 047 [arXiv:1301.0868] [INSPIRE].
Y. Geyer, A. E. Lipstein and L. J. Mason, Ambitwistor strings in four dimensions, Phys. Rev. Lett. 113 (2014) 081602 [arXiv:1404.6219] [INSPIRE].
M. Bianchi, H. Elvang and D. Z. Freedman, Generating tree amplitudes in N = 4 SYM and N = 8 SG, JHEP 09 (2008) 063 [arXiv:0805.0757] [INSPIRE].
F. Cachazo, P. Svrček and E. Witten, MHV vertices and tree amplitudes in gauge theory, JHEP 09 (2004) 006 [hep-th/0403047] [INSPIRE].
N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest quantum field theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [INSPIRE].
M. Spradlin, A. Volovich and C. Wen, Three applications of a bonus relation for gravity amplitudes, Phys. Lett. B 674 (2009) 69 [arXiv:0812.4767] [INSPIRE].
S. He, D. Nandan and C. Wen, Note on bonus relations for N = 8 supergravity tree amplitudes, JHEP 02 (2011) 005 [arXiv:1011.4287] [INSPIRE].
J. M. Drummond and L. Ferro, Yangians, grassmannians and T-duality, JHEP 07 (2010) 027 [arXiv:1001.3348] [INSPIRE].
J. M. Drummond and L. Ferro, The yangian origin of the grassmannian integral, JHEP 12 (2010) 010 [arXiv:1002.4622] [INSPIRE].
N. Arkani-Hamed, L. Rodina and J. Trnka, Locality and unitarity of scattering amplitudes from singularities and gauge invariance, Phys. Rev. Lett. 120 (2018) 231602 [arXiv:1612.02797] [INSPIRE].
L. Rodina, Uniqueness from locality and BCFW shifts, JHEP 09 (2019) 078 [arXiv:1612.03885] [INSPIRE].
L. Rodina, Uniqueness from gauge invariance and the Adler zero, JHEP 09 (2019) 084 [arXiv:1612.06342] [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].
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:1505.05886] [INSPIRE].
J. L. Bourjaily, E. Herrmann and J. Trnka, Prescriptive unitarity, JHEP 06 (2017) 059 [arXiv:1704.05460] [INSPIRE].
C. Cheung, On-shell recursion relations for generic theories, JHEP 03 (2010) 098 [arXiv:0808.0504] [INSPIRE].
B. Feng, J. Wang, Y. Wang and Z. Zhang, BCFW recursion relation with nonzero boundary contribution, JHEP 01 (2010) 019 [arXiv:0911.0301] [INSPIRE].
T. Cohen, H. Elvang and M. Kiermaier, On-shell constructibility of tree amplitudes in general field theories, JHEP 04 (2011) 053 [arXiv:1010.0257] [INSPIRE].
Q. Jin and B. Feng, Recursion relation for boundary contribution, JHEP 06 (2015) 018 [arXiv:1412.8170] [INSPIRE].
C. Cheung, C.-H. Shen and J. Trnka, Simple recursion relations for general field theories, JHEP 06 (2015) 118 [arXiv:1502.05057] [INSPIRE].
C. Cheung, K. Kampf, J. Novotny, C.-H. Shen and J. Trnka, On-shell recursion relations for effective field theories, Phys. Rev. Lett. 116 (2016) 041601 [arXiv:1509.03309] [INSPIRE].
K. Kampf, J. Novotny and J. Trnka, Recursion relations for tree-level amplitudes in the SU(N) nonlinear sigma model, Phys. Rev. D 87 (2013) 081701 [arXiv:1212.5224] [INSPIRE].
P. Benincasa and M. Parisi, Positive geometries and differential forms with non-logarithmic singularities. Part I, JHEP 08 (2020) 023 [arXiv:2005.03612] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2012.15780
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Trnka, J. Towards the Gravituhedron: new expressions for NMHV gravity amplitudes. J. High Energ. Phys. 2021, 253 (2021). https://doi.org/10.1007/JHEP04(2021)253
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2021)253