Abstract
Using the pure spinor master action for 10D super-Yang-Mills in the gauge b0V = QΞ, tree-level scattering amplitudes are calculated through the perturbiner method, and shown to match those obtained from pure spinor CFT techniques. We find kinematic numerators made of nested b-ghost operators, and show that the Siegel gauge condition b0V = 0 gives rise to color-kinematics duality satisfying numerators whose Jacobi identity follows from the Jacobi identity of a kinematic algebra.
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W. Siegel and M. Roček, On off-shell supermultiplets, Phys. Lett. B 105 (1981) 275 [INSPIRE].
J. G. Taylor, A No Go Theorem for Off-shell Extended Supergravities, J. Phys. A 15 (1982) 867 [INSPIRE].
V. O. Rivelles and J. G. Taylor, Off-shell No Go Theorems for Higher Dimensional Supersymmetries and Supergravities, Phys. Lett. B 121 (1983) 37 [INSPIRE].
B. E. W. Nilsson, Pure Spinors as Auxiliary Fields in the Ten-dimensional Supersymmetric Yang-Mills Theory, Class. Quant. Grav. 3 (1986) L41 [INSPIRE].
M. Cederwall, Superfield actions for N = 8 and N = 6 conformal theories in three dimensions, JHEP 10 (2008) 070 [arXiv:0809.0318] [INSPIRE].
M. Cederwall, D = 11 supergravity with manifest supersymmetry, Mod. Phys. Lett. A 25 (2010) 3201 [arXiv:1001.0112] [INSPIRE].
M. Cederwall and A. Karlsson, Pure spinor superfields and Born-Infeld theory, JHEP 11 (2011) 134 [arXiv:1109.0809] [INSPIRE].
M. Cederwall, Pure spinor superfields — an overview, Springer Proc. Phys. 153 (2014) 61 [arXiv:1307.1762] [INSPIRE].
N. Berkovits, Super Poincaré covariant quantization of the superstring, JHEP 04 (2000) 018 [hep-th/0001035] [INSPIRE].
C. R. Mafra, O. Schlotterer and S. Stieberger, Complete N-Point Superstring Disk Amplitude I. Pure Spinor Computation, Nucl. Phys. B 873 (2013) 419 [arXiv:1106.2645] [INSPIRE].
C. R. Mafra and O. Schlotterer, Towards the n-point one-loop superstring amplitude. Part I. Pure spinors and superfield kinematics, JHEP 08 (2019) 090 [arXiv:1812.10969] [INSPIRE].
C. R. Mafra and O. Schlotterer, Towards the n-point one-loop superstring amplitude. Part II. Worldsheet functions and their duality to kinematics, JHEP 08 (2019) 091 [arXiv:1812.10970] [INSPIRE].
E. D’Hoker, C. R. Mafra, B. Pioline and O. Schlotterer, Two-loop superstring five-point amplitudes. Part I. Construction via chiral splitting and pure spinors, JHEP 08 (2020) 135 [arXiv:2006.05270] [INSPIRE].
H. Gomez and C. R. Mafra, The closed-string 3-loop amplitude and S-duality, JHEP 10 (2013) 217 [arXiv:1308.6567] [INSPIRE].
W. Siegel, Covariantly Second Quantized String. 2, Phys. Lett. B 149 (1984) 157 [INSPIRE].
W. Siegel, Introduction to string field theory, Adv. Ser. Math. Phys. 8 (1988) 1.
M. Cederwall, From supergeometry to pure spinors, in 6th Summer School in Modern Mathematical Physics, Belgrade Serbia (2010), pg. 139 [arXiv:1012.3334] [INSPIRE].
J. Bjornsson and M. B. Green, 5 loops in 24/5 dimensions, JHEP 08 (2010) 132 [arXiv:1004.2692] [INSPIRE].
J. Bjornsson, Multi-loop amplitudes in maximally supersymmetric pure spinor field theory, JHEP 01 (2011) 002 [arXiv:1009.5906] [INSPIRE].
M. Cederwall and A. Karlsson, Loop amplitudes in maximal supergravity with manifest supersymmetry, JHEP 03 (2013) 114 [arXiv:1212.5175] [INSPIRE].
A. Karlsson, Ultraviolet divergences in maximal supergravity from a pure spinor point of view, JHEP 04 (2015) 165 [arXiv:1412.5983] [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].
N. E. J. Bjerrum-Bohr, P. H. Damgaard, T. Sondergaard and P. Vanhove, The Momentum Kernel of Gauge and Gravity Theories, JHEP 01 (2011) 001 [arXiv:1010.3933] [INSPIRE].
S. Lee, C. R. Mafra and O. Schlotterer, Non-linear gauge transformations in D = 10 SYM theory and the BCJ duality, JHEP 03 (2016) 090 [arXiv:1510.08843] [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 et al., Ultraviolet Properties of \( \mathcal{N} \) = 8 Supergravity at Five Loops, Phys. Rev. D 98 (2018) 086021 [arXiv:1804.09311] [INSPIRE].
R. Monteiro and D. O’Connell, The Kinematic Algebra From the Self-Dual Sector, JHEP 07 (2011) 007 [arXiv:1105.2565] [INSPIRE].
C. Cheung and C.-H. Shen, Symmetry for Flavor-Kinematics Duality from an Action, Phys. Rev. Lett. 118 (2017) 121601 [arXiv:1612.00868] [INSPIRE].
G. Chen, H. Johansson, F. Teng, and T. Wang, On the kinematic algebra for BCJ numerators beyond the MHV sector, JHEP 11 (2019) 055 [arXiv:1906.10683] [INSPIRE].
G. Chen, H. Johansson, F. Teng and T. Wang, Next-to-MHV Yang-Mills kinematic algebra, arXiv:2104.12726 [INSPIRE].
Z. Bern, T. Dennen, Y.-t. Huang and M. Kiermaier, Gravity as the Square of Gauge Theory, Phys. Rev. D 82 (2010) 065003 [arXiv:1004.0693] [INSPIRE].
M. Tolotti and S. Weinzierl, Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality, JHEP 07 (2013) 111 [arXiv:1306.2975] [INSPIRE].
L. Borsten, H. Kim, B. Jurčo, T. Macrelli, C. Saemann and M. Wolf, Double Copy from Homotopy Algebras, arXiv:2102.11390 [INSPIRE].
L. Borsten, B. Jurco, H. Kim, T. Macrelli, C. Saemann and M. Wolf, Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality, arXiv:2108.03030 [INSPIRE].
M. Reiterer, A homotopy BV algebra for Yang-Mills and color-kinematics, arXiv:1912.03110 [INSPIRE].
N. Berkovits, Covariant quantization of the superparticle using pure spinors, JHEP 09 (2001) 016 [hep-th/0105050] [INSPIRE].
J. P. Harnad and S. Shnider, Constraints and field equations for ten-dimensional superyang-mills theory, Commun. Math. Phys. 106 (1986) 183 [INSPIRE].
G. Policastro and D. Tsimpis, R4, purified, Class. Quant. Grav. 23 (2006) 4753 [hep-th/0603165] [INSPIRE].
N. Berkovits, ICTP lectures on covariant quantization of the superstring, ICTP Lect. Notes Ser. 13 (2003) 57 [hep-th/0209059] [INSPIRE].
N. Berkovits, Pure spinor formalism as an N = 2 topological string, JHEP 10 (2005) 089 [hep-th/0509120] [INSPIRE].
N. Berkovits, Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring, JHEP 09 (2004) 047 [hep-th/0406055] [INSPIRE].
N. Berkovits and N. Nekrasov, Multiloop superstring amplitudes from non-minimal pure spinor formalism, JHEP 12 (2006) 029 [hep-th/0609012] [INSPIRE].
N. Berkovits, Dynamical twisting and the b ghost in the pure spinor formalism, JHEP 06 (2013) 091 [arXiv:1305.0693] [INSPIRE].
F. A. Berends and W. T. Giele, Multiple Soft Gluon Radiation in Parton Processes, Nucl. Phys. B 313 (1989) 595 [INSPIRE].
K. G. Selivanov, On tree form-factors in (supersymmetric) Yang-Mills theory, Commun. Math. Phys. 208 (2000) 671 [hep-th/9809046] [INSPIRE].
C. R. Mafra and O. Schlotterer, Solution to the nonlinear field equations of ten dimensional supersymmetric Yang-Mills theory, Phys. Rev. D 92 (2015) 066001 [arXiv:1501.05562] [INSPIRE].
C. R. Mafra, O. Schlotterer, S. Stieberger and D. Tsimpis, A recursive method for SYM n-point tree amplitudes, Phys. Rev. D 83 (2011) 126012 [arXiv:1012.3981] [INSPIRE].
C. R. Mafra, Towards Field Theory Amplitudes From the Cohomology of Pure Spinor Superspace, JHEP 11 (2010) 096 [arXiv:1007.3639] [INSPIRE].
C. R. Mafra and O. Schlotterer, Berends-Giele recursions and the BCJ duality in superspace and components, JHEP 03 (2016) 097 [arXiv:1510.08846] [INSPIRE].
C. R. Mafra and O. Schlotterer, Multiparticle SYM equations of motion and pure spinor BRST blocks, JHEP 07 (2014) 153 [arXiv:1404.4986] [INSPIRE].
C. R. Mafra, PSS: A FORM Program to Evaluate Pure Spinor Superspace Expressions, arXiv:1007.4999 [INSPIRE].
C. R. Mafra and O. Schlotterer, Cohomology foundations of one-loop amplitudes in pure spinor superspace, arXiv:1408.3605 [INSPIRE].
C. Cheung and J. Mangan, Covariant Color-Kinematics Duality, arXiv:2108.02276 [INSPIRE].
N. E. J. Bjerrum-Bohr, J. L. Bourjaily, P. H. Damgaard and B. Feng, Manifesting Color-Kinematics Duality in the Scattering Equation Formalism, JHEP 09 (2016) 094 [arXiv:1608.00006] [INSPIRE].
Y.-J. Du and F. Teng, BCJ numerators from reduced Pfaffian, JHEP 04 (2017) 033 [arXiv:1703.05717] [INSPIRE].
C.-H. Fu, P. Vanhove and Y. Wang, A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator, JHEP 09 (2018) 141 [arXiv:1806.09584] [INSPIRE].
A. Edison and F. Teng, Efficient Calculation of Crossing Symmetric BCJ Tree Numerators, JHEP 12 (2020) 138 [arXiv:2005.03638] [INSPIRE].
N. Ahmadiniaz, F. M. Balli, C. Lopez-Arcos, A. Q. Velez and C. Schubert, Color-kinematics duality from the Bern-Kosower formalism, Phys. Rev. D 104 (2021) L041702 [arXiv:2105.06745] [INSPIRE].
E. Bridges and C. R. Mafra, Algorithmic construction of SYM multiparticle superfields in the BCJ gauge, JHEP 10 (2019) 022 [arXiv:1906.12252] [INSPIRE].
M. Chiodaroli, Q. Jin and R. Roiban, Color/kinematics duality for general abelian orbifolds of N = 4 super Yang-Mills theory, JHEP 01 (2014) 152 [arXiv:1311.3600] [INSPIRE].
M. Cederwall, An off-shell superspace reformulation of D = 4, N = 4 super-Yang-Mills theory, Fortsch. Phys. 66 (2018) 1700082 [arXiv:1707.00554] [INSPIRE].
M. Cederwall, Pure spinor superspace action for D = 6, N = 1 super-Yang-Mills theory, JHEP 05 (2018) 115 [arXiv:1712.02284] [INSPIRE].
M. Ben-Shahar and H. Johansson, Off-Shell Color-Kinematics Duality for Chern-Simons, in preparation.
N. Berkovits and M. Guillen, Equations of motion from Cederwall’s pure spinor superspace actions, JHEP 08 (2018) 033 [arXiv:1804.06979] [INSPIRE].
M. Guillen, Notes on the 11D pure spinor wordline vertex operators, JHEP 08 (2020) 122 [arXiv:2006.06022] [INSPIRE].
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Ben-Shahar, M., Guillen, M. 10D super-Yang-Mills scattering amplitudes from its pure spinor action. J. High Energ. Phys. 2021, 14 (2021). https://doi.org/10.1007/JHEP12(2021)014
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DOI: https://doi.org/10.1007/JHEP12(2021)014