Built on

C. Marboe and E. Widen, “The fate of the Konishi multiplet in the β \beta -deformed Quantum Spectral Curve,” arXiv:1902.01248 [hep-th]
Original
1902
Earlier work this paper cites.
N. Gromov and A. Sever, “Derivation of the Holographic Dual of a Planar Conformal Field Theory in 4D,” Phys. Rev. Lett. 123
Original
1903
Earlier work this paper cites.
R. N. Lee and A. I. Onishchenko, “ABJM quantum spectral curve at twist 1: algorithmic perturbative solution,” arXiv:1905.03116 [hep-th]
Original
1905
Earlier work this paper cites.
Y. Jiang, S. Komatsu and E. Vescovi, “Structure Constants in 𝒩 = 4 \mathcal{N}=4 SYM at Finite Coupling as Worldsheet g g -Function,” arXiv:1906.07733 [hep-th]
Original
1906
Earlier work this paper cites.
A. Cavaglia, N. Gromov and F. Levkovich-Maslyuk, “Separation of variables and scalar products at any rank,” JHEP 1909
Original
1907
Earlier work this paper cites.
N. Gromov and A. Sever, “Quantum Fishchain in A d S 5 AdS_{5} ,” arXiv:1907.01001 [hep-th]
Original
1907
Earlier work this paper cites.
J. M. Maillet, G. Niccoli and L. Vignoli, “Separation of variables bases for integrable g l ℳ | 𝒩 gl_{\mathcal{M}|\mathcal{N}} and Hubbard models,” arXiv:1907.08124 [math-ph]
Original
1907
Earlier work this paper cites.
Y. Jiang, S. Komatsu and E. Vescovi, “Exact Three-Point Functions of Determinant Operators in Planar N = 4 N=4 Supersymmetric Yang-Mills Theory,” arXiv:1907.11242 [hep-th]
Original
1907
Earlier work this paper cites.
N. Gromov and A. Sever, “The Holographic Dual of Strongly γ \gamma -deformed N=4 SYM Theory: Derivation, Generalization, Integrability and Discrete Reparametrization Symmetry,” arXiv:1908.10379 [hep-th]
Original
1908
Earlier work this paper cites.
E. Granet and J. L. Jacobsen, “On zero-remainder conditions in the Bethe ansatz,” arXiv:1910.07797 [hep-th]
Original
1910
Earlier work this paper cites.
N. Drukker et al
Original
1910
Earlier work this paper cites.
N. Gromov, F. Levkovich-Maslyuk, P. Ryan and D. Volin, “Dual Separated Variables and Scalar Products,” arXiv:1910.13442 [hep-th]
Original
1910
Earlier work this paper cites.
D. Correa, J. Maldacena and A. Sever, “The quark anti-quark potential and the cusp anomalous dimension from a TBA equation,” JHEP 1208
Original
1913
Earlier work this paper cites.
N. Gromov, V. Kazakov, S. Leurent and D. Volin, “Quantum Spectral Curve for Planar 𝒩 = 4 \mathcal{N}=4 Super-Yang-Mills Theory,” Phys. Rev. Lett. 112
Original
1939
Earlier work this paper cites.
N. Gromov, F. Levkovich-Maslyuk and G. Sizov, “Analytic Solution of Bremsstrahlung TBA II: Turning on the Sphere Angle,” JHEP 1310
Original
1944
Earlier work this paper cites.
B. Sutherland, “A General Model for Multicomponent Quantum Systems,” Phys. Rev. B12
1975
Earlier work this paper cites.
P. P. Kulish and N. Y. Reshetikhin, “Generalized Heisenberg Ferromagnet And The Gross-neveu Model,” Sov. Phys. JETP 53
1981
Earlier work this paper cites.
P. P. Kulish and N. Y. Reshetikhin, “Diagonalization Of Gl(n) Invariant Transfer Matrices And Quantum N Wave System (lee Model),” J. Phys. A 16
1983
Earlier work this paper cites.
P. P. Kulish, “Integrable graded magnets,” J. Sov. Math. 35
1985
Earlier work this paper cites.
E. K. Sklyanin, “Quantum inverse scattering method. Selected topics,” In: Quantum Group and Quantum Integrable Systems: Nankai Lectures on Mathematical Physics : Nankai Institute of Mathematics, China 2-18 April 1991 (World Scientific 1992), pp 63-97 [hep-th/9211111]
1992
Earlier work this paper cites.
E. K. Sklyanin, “Separation of variables in the quantum integrable models related to the Yangian Y[sl(3)],” J. Math. Sci. 80
1993
Earlier work this paper cites.
E. K. Sklyanin, “Separation of variables - new trends,” Prog. Theor. Phys. Suppl. 118
1995
Earlier work this paper cites.
I. Krichever, O. Lipan, P. Wiegmann and A. Zabrodin, “Quantum integrable systems and elliptic solutions of classical discrete nonlinear equations,” Commun. Math. Phys. 188
1997
Earlier work this paper cites.
V. V. Bazhanov, S. L. Lukyanov and A. B. Zamolodchikov, “Integrable structure of conformal field theory. 2. Q operator and DDV equation,” Commun. Math. Phys. 190
1997
Earlier work this paper cites.
J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity,” Int. J. Theor. Phys. 38
1998
Earlier work this paper cites.
E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from noncritical string theory,” Phys. Lett. B 428
1998
Earlier work this paper cites.
G. P. Pronko and Y. G. Stroganov, “The Complex of solutions of the nested Bethe ansatz. The A(2) spin chain,” J. Phys. A 33
2000
Earlier work this paper cites.
J. K. Erickson, G. W. Semenoff, R. J. Szabo and K. Zarembo, “Static potential in N=4 supersymmetric Yang-Mills theory,” Phys. Rev. D 61
2000
Earlier work this paper cites.
J. K. Erickson, G. W. Semenoff and K. Zarembo, “Wilson loops in N=4 supersymmetric Yang-Mills theory,” Nucl. Phys. B 582
2000
Earlier work this paper cites.
F. Smirnov, V. Zeitlin, “On The Quantization of Affine Jacobi Varieties of Spectral Curves”. Statistical Field Theories. - Springer, Dordrecht, 2002, p. 79-89
2002
Earlier work this paper cites.
J. A. Minahan and K. Zarembo, “The Bethe ansatz for N=4 superYang-Mills,” JHEP 0303
2003
Earlier work this paper cites.

Similar

I. Bena, J. Polchinski and R. Roiban, “Hidden symmetries of the AdS(5) x S**5 superstring,” Phys. Rev. D 69
2004
Cited alongside, same era.
N. Beisert and M. Staudacher, “Long-range psu(2,2|4) Bethe Ansatze for gauge theory and strings,” Nucl. Phys. B 727
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F. H. L. Essler, H. Frahm, F. Goehmann, A. Kluemper, and V. E. Korepin, The One-Dimensional Hubbard Model, Cambridge University Press (2005)
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Cited alongside, same era.
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Cited alongside, same era.
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2007
Cited alongside, same era.

Then

L. Anselmetti, D. Bombardelli, A. Cavaglià and R. Tateo, “12 loops and triple wrapping in ABJM theory from integrability,” JHEP 1510
Original
2015
Later among the works it cites.
D. Bombardelli et al
Original
2016
Later among the works it cites.
V. Kazakov, S. Leurent and D. Volin, “T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve,” JHEP 1612
Original
2016
Later among the works it cites.
F. Levkovich-Maslyuk, “The Bethe ansatz,” J. Phys. A 49
Original
2016
Later among the works it cites.
C. Marboe and V. Velizhanin, “Twist-2 at seven loops in planar 𝒩 \mathcal{N} = 4 SYM theory: full result and analytic properties,” JHEP 1611
Original

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2019

A review of the AdS/CFT Quantum Spectral Curve

Levkovich-Maslyuk, Fedor

Understand

We give an introduction to the Quantum Spectral Curve in AdS/CFT.

This is an integrability-based framework which provides the exact spectrum of planar N = 4 super Yang-Mills theory (and of the dual string model) in terms of a solution of a Riemann-Hilbert problem for a finite set of functions.
We review the underlying QQ relations starting from simple spin chain examples, and describe the special features arising for AdS/CFT.
We also discuss the recently found links between the Quantum Spectral Curve and the computation of correlation functions.

Built on

C. Marboe and E. Widen, “The fate of the Konishi multiplet in the β \beta -deformed Quantum Spectral Curve,” arXiv:1902.01248 [hep-th]
Original
1902
Earlier work this paper cites.
N. Gromov and A. Sever, “Derivation of the Holographic Dual of a Planar Conformal Field Theory in 4D,” Phys. Rev. Lett. 123
Original
1903
Earlier work this paper cites.
R. N. Lee and A. I. Onishchenko, “ABJM quantum spectral curve at twist 1: algorithmic perturbative solution,” arXiv:1905.03116 [hep-th]
Original
1905
Earlier work this paper cites.
Y. Jiang, S. Komatsu and E. Vescovi, “Structure Constants in 𝒩 = 4 \mathcal{N}=4 SYM at Finite Coupling as Worldsheet g g -Function,” arXiv:1906.07733 [hep-th]
Original
1906
Earlier work this paper cites.
A. Cavaglia, N. Gromov and F. Levkovich-Maslyuk, “Separation of variables and scalar products at any rank,” JHEP 1909
Original
1907
Earlier work this paper cites.
N. Gromov and A. Sever, “Quantum Fishchain in A d S 5 AdS_{5} ,” arXiv:1907.01001 [hep-th]
Original
1907
Earlier work this paper cites.
J. M. Maillet, G. Niccoli and L. Vignoli, “Separation of variables bases for integrable g l ℳ | 𝒩 gl_{\mathcal{M}|\mathcal{N}} and Hubbard models,” arXiv:1907.08124 [math-ph]
Original
1907
Earlier work this paper cites.
Y. Jiang, S. Komatsu and E. Vescovi, “Exact Three-Point Functions of Determinant Operators in Planar N = 4 N=4 Supersymmetric Yang-Mills Theory,” arXiv:1907.11242 [hep-th]
Original
1907
Earlier work this paper cites.
N. Gromov and A. Sever, “The Holographic Dual of Strongly γ \gamma -deformed N=4 SYM Theory: Derivation, Generalization, Integrability and Discrete Reparametrization Symmetry,” arXiv:1908.10379 [hep-th]
Original
1908
Earlier work this paper cites.
E. Granet and J. L. Jacobsen, “On zero-remainder conditions in the Bethe ansatz,” arXiv:1910.07797 [hep-th]
Original
1910
Earlier work this paper cites.
N. Drukker et al
Original
1910
Earlier work this paper cites.
N. Gromov, F. Levkovich-Maslyuk, P. Ryan and D. Volin, “Dual Separated Variables and Scalar Products,” arXiv:1910.13442 [hep-th]
Original
1910
Earlier work this paper cites.
D. Correa, J. Maldacena and A. Sever, “The quark anti-quark potential and the cusp anomalous dimension from a TBA equation,” JHEP 1208
Original
1913
Earlier work this paper cites.
N. Gromov, V. Kazakov, S. Leurent and D. Volin, “Quantum Spectral Curve for Planar 𝒩 = 4 \mathcal{N}=4 Super-Yang-Mills Theory,” Phys. Rev. Lett. 112
Original
1939
Earlier work this paper cites.
N. Gromov, F. Levkovich-Maslyuk and G. Sizov, “Analytic Solution of Bremsstrahlung TBA II: Turning on the Sphere Angle,” JHEP 1310
Original
1944
Earlier work this paper cites.
B. Sutherland, “A General Model for Multicomponent Quantum Systems,” Phys. Rev. B12
1975
Earlier work this paper cites.
P. P. Kulish and N. Y. Reshetikhin, “Generalized Heisenberg Ferromagnet And The Gross-neveu Model,” Sov. Phys. JETP 53
1981
Earlier work this paper cites.
P. P. Kulish and N. Y. Reshetikhin, “Diagonalization Of Gl(n) Invariant Transfer Matrices And Quantum N Wave System (lee Model),” J. Phys. A 16
1983
Earlier work this paper cites.
P. P. Kulish, “Integrable graded magnets,” J. Sov. Math. 35
1985
Earlier work this paper cites.
E. K. Sklyanin, “Quantum inverse scattering method. Selected topics,” In: Quantum Group and Quantum Integrable Systems: Nankai Lectures on Mathematical Physics : Nankai Institute of Mathematics, China 2-18 April 1991 (World Scientific 1992), pp 63-97 [hep-th/9211111]
1992
Earlier work this paper cites.
E. K. Sklyanin, “Separation of variables in the quantum integrable models related to the Yangian Y[sl(3)],” J. Math. Sci. 80
1993
Earlier work this paper cites.
E. K. Sklyanin, “Separation of variables - new trends,” Prog. Theor. Phys. Suppl. 118
1995
Earlier work this paper cites.
I. Krichever, O. Lipan, P. Wiegmann and A. Zabrodin, “Quantum integrable systems and elliptic solutions of classical discrete nonlinear equations,” Commun. Math. Phys. 188
1997
Earlier work this paper cites.
V. V. Bazhanov, S. L. Lukyanov and A. B. Zamolodchikov, “Integrable structure of conformal field theory. 2. Q operator and DDV equation,” Commun. Math. Phys. 190
1997
Earlier work this paper cites.
J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity,” Int. J. Theor. Phys. 38
1998
Earlier work this paper cites.
E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from noncritical string theory,” Phys. Lett. B 428
1998
Earlier work this paper cites.
G. P. Pronko and Y. G. Stroganov, “The Complex of solutions of the nested Bethe ansatz. The A(2) spin chain,” J. Phys. A 33
2000
Earlier work this paper cites.
J. K. Erickson, G. W. Semenoff, R. J. Szabo and K. Zarembo, “Static potential in N=4 supersymmetric Yang-Mills theory,” Phys. Rev. D 61
2000
Earlier work this paper cites.
J. K. Erickson, G. W. Semenoff and K. Zarembo, “Wilson loops in N=4 supersymmetric Yang-Mills theory,” Nucl. Phys. B 582
2000
Earlier work this paper cites.
F. Smirnov, V. Zeitlin, “On The Quantization of Affine Jacobi Varieties of Spectral Curves”. Statistical Field Theories. - Springer, Dordrecht, 2002, p. 79-89
2002
Earlier work this paper cites.
J. A. Minahan and K. Zarembo, “The Bethe ansatz for N=4 superYang-Mills,” JHEP 0303
2003
Earlier work this paper cites.

Similar

I. Bena, J. Polchinski and R. Roiban, “Hidden symmetries of the AdS(5) x S**5 superstring,” Phys. Rev. D 69
2004
Cited alongside, same era.
N. Beisert and M. Staudacher, “Long-range psu(2,2|4) Bethe Ansatze for gauge theory and strings,” Nucl. Phys. B 727
2005
Cited alongside, same era.
F. H. L. Essler, H. Frahm, F. Goehmann, A. Kluemper, and V. E. Korepin, The One-Dimensional Hubbard Model, Cambridge University Press (2005)
2005
Cited alongside, same era.
P. Dorey, C. Dunning, D. Masoero, J. Suzuki and R. Tateo, “Pseudo-differential equations, and the Bethe ansatz for the classical Lie algebras,” Nucl. Phys. B 772
2007
Cited alongside, same era.
O. Babelon, “A short introduction to classical and quantum integrable systems,” Lectures given at IPhT Saclay (2007)
2007
Cited alongside, same era.