2013

Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes

Frassek, Rouven, Kanning, Nils, Ko, Yumi et al.

Understand

We propose that Baxter's Z-invariant six-vertex model at the rational gl(2) point on a planar but in general not rectangular lattice provides a way to study Yangian invariants.

These are identified with eigenfunctions of certain monodromies of an auxiliary inhomogeneous spin chain.
As a consequence they are special solutions to the eigenvalue problem of the associated transfer matrix.
Excitingly, this allows to construct them using Bethe ansatz techniques.

Built on

H. Bethe, “Zur Theorie der Metalle. I. Eigenwerte und Eigenfunktionen der Linearen Atomkette,” Z. Phys
1931
Earlier work this paper cites.
P. A. M. Dirac, “Quantum Electrodynamics,” Commun. Dublin Inst. Adv. Stud. A
1943
Earlier work this paper cites.
V. Bargmann, “On a Hilbert Space of Analytic Functions and an Associated Integral Transform Part I,” Commun. Pure Appl. Math
1961
Earlier work this paper cites.
Dover Publications, 1964
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions · 1964
Earlier work this paper cites.
E. H. Lieb, “Residual Entropy of Square Ice,” Phys. Rev
1967
Earlier work this paper cites.
E. H. Lieb, “Exact Solution of the F Model of an Antiferroelectric,” Phys. Rev. Lett
1967
Earlier work this paper cites.
B. Sutherland, “Exact Solution of a Two-Dimensional Model for Hydrogen-Bonded Crystals,” Phys. Rev. Lett
1967
Earlier work this paper cites.
C. N. Yang, “Some Exact Results for the Many Body Problems in One Dimension with Repulsive Delta Function Interaction,” Phys. Rev. Lett
1967
Earlier work this paper cites.
M. Gaudin, “Un Systeme a Une Dimension de Fermions en Interaction,” Phys. Lett. A
1967
Earlier work this paper cites.
R. J. Baxter, “Partition Function of the Eight-Vertex Lattice Model,” Ann. Phys
1972
Earlier work this paper cites.
R. J. Baxter, “Solvable Eight Vertex Model on an Arbitrary Planar Lattice,” Phil. Trans. Roy. Soc. Lond. A
1978
Earlier work this paper cites.
B. Berg, M. Karowski, P. Weisz, and V. Kurak, “Factorized U(n) Symmetric S-Matrices in Two Dimensions,” Nucl. Phys. B
1978
Earlier work this paper cites.
Addison-Wesley Publishing, 1981
L. C. Biedenharn and J. D. Louck, Angular Momentum in Quantum Physics · 1981
Earlier work this paper cites.
P. P. Kulish, N. Y. Reshetikhin, and E. K. Sklyanin, “Yang-Baxter Equation and Representation Theory: I,” Lett. Math. Phys
1981
Earlier work this paper cites.
P. P. Kulish and N. Y. Reshetikhin, “Diagonalisation of GL(N) Invariant Transfer Matrices and Quantum N-Wave System (Lee Model),” J. Phys. A
1983
Earlier work this paper cites.
H. J. de Vega, H. Eichenherr, and J. M. Maillet, “Yang-Baxter Algebras of Monodromy Matrices in Integrable Quantum Field Theories,” Nucl. Phys. B
1984
Earlier work this paper cites.
H. Fan, Z. Liu, and T. Ruan, “Does the Creation Operator a+ Possess Eigenvectors?,” Commun. Theor. Phys
1984
Earlier work this paper cites.
V. Drinfeld, “Hopf Algebras and the Quantum Yang-Baxter Equation,” Sov. Math. Dokl
1985
Earlier work this paper cites.
R. J. Baxter, “Perimeter Bethe Ansatz,” J. Phys. A
1987
Earlier work this paper cites.
L. V. Avdeev and A. A. Vladimirov, “On Exceptional Solutions of the Bethe Ansatz Equations,” Theor. Math. Phys
1987
Earlier work this paper cites.
V. G. Drinfeld, “Quantum Groups,” J. Sov. Math
1988
Earlier work this paper cites.
A. B. Zamolodchikov, “Integrable Field Theory from Conformal Field Theory,” Adv. Stud. Pure Math
1989
Earlier work this paper cites.
Kluwer, 1991
Original
J. A. Dubinskii, Analytic Pseudo-Differential Operators and their Applications · 1991
Earlier work this paper cites.

Similar

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1992
Cited alongside, same era.
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1993
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C. Destri and H. J. de Vega, “Yang-Baxter Symmetry in Integrable Models: New Light from the Bethe Ansatz Solution,” Nucl. Phys. B
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F. Hong-Yi and J. R. Klauder, “On the Common Eigenvectors of Two-Mode Creation Operators and the Charge Operator,” Mod. Phys. Lett. A
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1995
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M. Karbach and G. Müller, “Introduction to the Bethe Ansatz I,” Phys. Comp
1997
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Springer, 1997
P. Dorey, “Exact S-Matrices,” in Conformal Field Theories and Integrable Models · 1997
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North-Holland Publishing, 1998
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Then

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F. H. L. Essler, H. Frahm, F. Göhmann, A. Klümper, and V. E. Korepin, The One-Dimensional Hubbard Model · 2010
Later among the works it cites.
J. M. Drummond and L. Ferro, “Yangians, Grassmannians and T-duality,” JHEP
Original
2010
Later among the works it cites.
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Original
2010
Later among the works it cites.
N. Arkani-Hamed, F. Cachazo, C. Cheung, and J. Kaplan, “The S-Matrix in Twistor Space,” JHEP
Original
2010
Later among the works it cites.
A. A. Ovchinnikov, “Coordinate Space Wave Function from the Algebraic Bethe Ansatz for the Inhomogeneous Six-Vertex Model,” Phys. Lett. A
Original
2010
Later among the works it cites.
World Scientific Publishing, 2011
Original
N. Beisert, “On Yangian Symmetry in Planar N=4 SYM,” in Gribov-80 Memorial Volume: Quantum Chromodynamics and Beyond · 2011
Later among the works it cites.
J. M. Drummond, “Tree-Level Amplitudes and Dual Superconformal Symmetry,” J. Phys. A
Original
2011
Later among the works it cites.
T. Bargheer, N. Beisert, and F. Loebbert, “Exact Superconformal and Yangian Symmetry of Scattering Amplitudes,” J. Phys. A
Original
2011
Later among the works it cites.
V. V. Bazhanov, R. Frassek, T. Łukowski, C. Meneghelli, and M. Staudacher, “Baxter Q-Operators and Representations of Yangians,” Nucl. Phys. B
Original
2011
Later among the works it cites.
R. Frassek, T. Łukowski, C. Meneghelli, and M. Staudacher, “Oscillator Construction of su(n|m) Q-Operators,” Nucl. Phys. B
Original
2011
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Original
2012
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Original
2012
Later among the works it cites.
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Original
2012
Later among the works it cites.
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Original
2013
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G. Papathanasiou, “Hexagon Wilson Loop OPE and Harmonic Polylogarithms,” JHEP
Original
2013
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L. Ferro, T. Łukowski, C. Meneghelli, J. Plefka, and M. Staudacher, “Harmonic R Matrices for Scattering Amplitudes and Spectral Regularization,” Phys. Rev. Lett
Original
2013
Closest in time.
Cambridge University Press, 2013
L. Samaj and Z. Bajnok, Introduction to the Statistical Physics of Integrable Many-Body Systems · 2013
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D. Chicherin and R. Kirschner, “Yangian Symmetric Correlators,” Nucl. Phys. B
Original
2013
Closest in time.
R. I. Nepomechie and C. Wang, “Algebraic Bethe Ansatz for Singular Solutions,” J. Phys. A
Original
2013
Closest in time.
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Original
2013
Closest in time.
R. Frassek and C. Meneghelli, “From Baxter Q-Operators to Local Charges,” J. Stat. Mech
Original
2013
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B. Basso, A. Sever, and P. Vieira, “Space-Time S-Matrix and Flux Tube S-Matrix II. Extracting and Matching Data,” arXiv:1306.2058
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2058
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