BCJ, worldsheet quantum algebra and KZ equations

H. Johansson and A. Ochirov, “Double copy for massive quantum particles with spin,” JHEP 09

Original

1906

Earlier work this paper cites.

G. Chen, H. Johansson, F. Teng and T. Wang, “On the kinematic algebra for BCJ numerators beyond the MHV sector,” JHEP 11

Original

1906

Earlier work this paper cites.

S. Mizera, “Aspects of Scattering Amplitudes and Moduli Space Localization,” [arXiv:1906.02099 [hep-th]]

Original

1906

Earlier work this paper cites.

Y. Geyer, R. Monteiro and R. Stark-Muchão, “Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality,” JHEP 12

Original

1908

Earlier work this paper cites.

Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson and R. Roiban, “The Duality Between Color and Kinematics and its Applications,” [arXiv:1909.01358 [hep-th]]

Original

1909

Earlier work this paper cites.

E. Casali, S. Mizera and P. Tourkine, “Monodromy relations from twisted homology,” JHEP 12

Original

1910

Earlier work this paper cites.

H. Frost and L. Mason, “Lie Polynomials and a Twistorial Correspondence for Amplitudes,” [arXiv:1912.04198 [hep-th]]

Original

1912

Earlier work this paper cites.

A. Kaderli, “A note on the Drinfeld associator for genus-zero superstring amplitudes in twisted de Rham theory,” [arXiv:1912.09406 [hep-th]]

Original

1912

Earlier work this paper cites.

Z. Bern, C. Boucher-Veronneau and H. Johansson, “N ¿= 4 Supergravity Amplitudes from Gauge Theory at One Loop,” Phys. Rev. D 84

Original

1935

Earlier work this paper cites.

E. Plahte, “Symmetry properties of dual tree-graph n-point amplitudes,” Nuovo Cim. A 66

1970

Earlier work this paper cites.

E. Del Giudice, P. Di Vecchia and S. Fubini, “General properties of the dual resonance model,” Annals Phys. 70

1972

Earlier work this paper cites.

L. A. Takhtajan and L. D. Faddeev, “The Quantum method of the inverse problem and the Heisenberg XYZ model,” Russ. Math. Surveys 34

1979

Earlier work this paper cites.

L. D. Faddeev, E. K. Sklyanin and L. A. Takhtajan, “The Quantum Inverse Problem Method. 1,” Theor. Math. Phys. 40

1980

Earlier work this paper cites.

L. D. Faddeev, “Quantum completely integral models of field theory,” Sov. Sci. Rev. C 1

1980

Earlier work this paper cites.

I. B. Frenkel and V. G. Kac, “Basic Representations of Affine Lie Algebras and Dual Resonance Models,” Invent. Math. 62

1980

Earlier work this paper cites.

B. Feigin and D. Fuks, “Invariant skew symmetric differential operators on the line and verma modules over the Virasoro algebra,” Funct. Anal. Appl. 16

1982

Earlier work this paper cites.

V. Drinfeld, “Hamiltonian structures of lie groups, lie bialgebras and the geometric meaning of the classical Yang-Baxter equations,” Sov. Math. Dokl. 27

1983

Earlier work this paper cites.

V. Knizhnik and A. Zamolodchikov, “Current Algebra and Wess-Zumino Model in Two-Dimensions,” Nucl. Phys. B 247

1984

Earlier work this paper cites.

V. Dotsenko and V. Fateev, “Conformal Algebra and Multipoint Correlation Functions in Two-Dimensional Statistical Models,” Nucl. Phys. B 240

1984

Earlier work this paper cites.

V. Dotsenko and V. Fateev, “Four Point Correlation Functions and the Operator Algebra in the Two-Dimensional Conformal Invariant Theories with the Central Charge c ¡ 1,” Nucl. Phys. B 251

1985

Earlier work this paper cites.

M. Jimbo, “A q difference analog of U(g) and the Yang-Baxter equation,” Lett. Math. Phys. 10

1985

Earlier work this paper cites.

V. Drinfeld, “Hopf algebras and the quantum Yang-Baxter equation,” Sov. Math. Dokl. 32

1985

Earlier work this paper cites.

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

Earlier work this paper cites.

M. Jimbo, “A q Analog of u (Gl (n+1)), Hecke Algebra and the Yang-Baxter Equation,” Lett. Math. Phys. 11

1986

Earlier work this paper cites.

T. Kohno, “Monodromy representations of braid groups and Yang-Baxter equations,” Annales de l’Institut Fourier, Volume 37 (1987) no. 4, pp. 139-160. doi : 10.5802/aif.1114. https://aif.centre-mersenne.org/item/AIF_1987__37_4_139_0/

1987

Earlier work this paper cites.

S. L. Woronowicz, “Compact matrix pseudogroups,” Commun. Math. Phys. 111

1987

Earlier work this paper cites.

S. L. Woronowicz, “Twisted SU(2) group: An Example of a noncommutative differential calculus,” Publ. Res. Inst. Math. Sci. Kyoto 23

1987

Earlier work this paper cites.

V. Drinfeld, “Quantum groups,” J. Sov. Math. 41

1988

Earlier work this paper cites.

Yu. I. Manin, “Quantum Groups and Non-commutative Geometry,” Centre de recherches mathématiques, Université de Montréal, 1988

1988

Earlier work this paper cites.

D. J. Gross and P. F. Mende, “String Theory Beyond the Planck Scale,” Nucl. Phys. B 303

1988

Earlier work this paper cites.

L. D. Faddeev, N. Y. Reshetikhin and L. A. Takhtajan, “Quantization of Lie Groups and Lie Algebras,” Alg. Anal. 1

1989

Earlier work this paper cites.

Y. I. Manin, “Multiparametric quantum deformation of the general linear supergroup,” Commun. Math. Phys. 123

1989

Earlier work this paper cites.

V. Drinfeld, “Quasi Hopf algebras,” Alg. Anal. 1N6

1990

Earlier work this paper cites.

A. Kirillov and N. Reshetikhin, “Representations of the algebra U(q)(sl(2, q orthogonal polynomials and invariants of links,” Adv. Series in Math. Phys. New Developments in the Theory of Knots 11 (1990) 202-256

1990

Earlier work this paper cites.

V. Schechtman, A. Varchenko, “Arrangements of hyperplanes and Lie algebra homology”. Invent Math 106, 139–194 (1991). https://doi.org/10.1007/BF01243909

1991

Earlier work this paper cites.

A. Varchenko, “Multidimensional Hypergeometric Functions The Representation Theory Of Lie Algebras And Quantum Groups,” Adv. Ser. Math. Phys., 21

1995

Earlier work this paper cites.

V. Del Duca, L. J. Dixon and F. Maltoni, “New color decompositions for gauge amplitudes at tree and loop level,” Nucl. Phys. B 571

2000

Earlier work this paper cites.

Varchenko, Aleksandr Nikolaevich. Special functions, KZ type equations, and representation theory. Vol. 98. American Mathematical Soc., 2003

2003

Earlier work this paper cites.

P. Srisangyingcharoen and P. Mansfield, [arXiv:2005.01712 [hep-th]]

Original

2005

Cited alongside, same era.

Z. Bern, J. Carrasco and H. Johansson, “New Relations for Gauge-Theory Amplitudes,” Phys. Rev. D 78

Original

2008

Cited alongside, same era.

Z. Bern, J. J. Carrasco, L. J. Dixon, H. Johansson and R. Roiban, “The Ultraviolet Behavior of N=8 Supergravity at Four Loops,” Phys. Rev. Lett. 103

Original

2009

Cited alongside, same era.

N. Bjerrum-Bohr, P. H. Damgaard and P. Vanhove, “Minimal Basis for Gauge Theory Amplitudes,” Phys. Rev. Lett. 103

Original

2009

Cited alongside, same era.

J. M. Drummond, J. M. Henn and J. Plefka, “Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory,” JHEP 05

D. Chicherin, S. Derkachov and R. Kirschner, “Yang-Baxter operators and scattering amplitudes in N=4 super-Yang-Mills theory,” Nucl. Phys. B 881

Original

2014

Later among the works it cites.

J. Broedel, O. Schlotterer, S. Stieberger and T. Terasoma, “All order α ′ \alpha^{\prime} -expansion of superstring trees from the Drinfeld associator,” Phys. Rev. D 89

Original

2014

Later among the works it cites.

F. Cachazo, S. He and E. Y. Yuan, “Scattering of Massless Particles: Scalars, Gluons and Gravitons,” JHEP 07

Original

2014

Later among the works it cites.

H. Johansson and A. Ochirov, “Pure Gravities via Color-Kinematics Duality for Fundamental Matter,” JHEP 11

Original

2015

Later among the works it cites.

M. Chiodaroli, M. Günaydin, H. Johansson and R. Roiban, “Scattering amplitudes in 𝒩 = 2 \mathcal{N}=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity,” JHEP 01