Supersymmetric Bethe ansatz and Baxter equations from discrete Hirota dynamics

Казаков, Владимир; Сорин, А.С.; Zabrodin, A.

doi:10.1016/j.nuclphysb.2007.06.025

Cited by 133 publications

(347 citation statements)

References 60 publications

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“…In the Heisenberg spin chains the Q-system appears as a set of Q-operators, or their eigenvalues -Q-functions, satisfying the Baxter-type functional equations appearing on various stages of Bäcklund reduction (or equivalently, the nesting procedure [28][29][30]) of the corresponding T-system [31][32][33]. It was pointed out in [31] that, for a system with su(n) symmetry, the set of all 2 n Q-functions can be identified with Plücker coordinates on finite-dimensional Grassmanians G k n , k = 0, 1, .…”

Section: Q-system -General Algebraic Descriptionmentioning

confidence: 99%

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Quantum spectral curve for arbitrary state/operator in AdS5/CFT4

Gromov

Казаков

Leurent

et al. 2015

J. High Energ. Phys.

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193

519

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We give a derivation of quantum spectral curve (QSC) -a finite set of Riemann-Hilbert equations for exact spectrum of planar N = 4 SYM theory proposed in our recent paper Phys. Rev. Lett. 112 (2014). We also generalize this construction to all local single trace operators of the theory, in contrast to the TBA-like approaches worked out only for a limited class of states. We reveal a rich algebraic and analytic structure of the QSC in terms of a so called Q-system -a finite set of Baxter-like Q-functions. This new point of view on the finite size spectral problem is shown to be completely compatible, though in a far from trivial way, with already known exact equations (analytic Y-system/TBA, or FiNLIE). We use the knowledge of this underlying Q-system to demonstrate how the classical finite gap solutions and the asymptotic Bethe ansatz emerge from our formalism in appropriate limits.

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Section: Q-system -General Algebraic Descriptionmentioning

confidence: 99%

“…The Q-system can be defined by a set of so-called Plücker's QQ-relations [11,32] (see also [36,37]), which is a set of bilinear constraints on 20 In certain more mathematically-oriented literature, the name Q-system is used for a different object:…”

Section: Definition Of Q-system and Qq-relationsmentioning

confidence: 99%

Quantum spectral curve for arbitrary state/operator in AdS5/CFT4

Gromov

Казаков

Leurent

et al. 2015

J. High Energ. Phys.

Self Cite

193

519

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“…Another constraint which we will impose is Q H " 1. In the rational (super)-spin chains Q H is the Baxter Q-function on the final step of the Bäcklund procedure [35,36], where it corresponds to the trivial glp0|0q sub-algebra and therefore it is naturally represented by a constant that does not depend on the spectral parameter. The same observation holds when Q-functions are constructed from the first principles, i.e.…”

Section: Jhep07(2012)023mentioning

confidence: 99%

“…For that we use the Plücker relations which follow from (4.14) and are explicitly given in [18,20,36]:…”

Section: Jhep07(2012)023mentioning

confidence: 99%

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Solving the AdS/CFT Y-system

Gromov

Казаков

Leurent³

et al. 2012

J. High Energ. Phys.

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297

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Using integrability and analyticity properties of the AdS 5 /CFT 4 Y-system we reduce it to a finite set of nonlinear integral equations. The Z 4 symmetry of the underlying coset sigma model, in its quantum version, allows for a deeper insight into the analyticity structure of the corresponding Y-functions and T-functions, as well as for their analyticity friendly parameterization in terms of Wronskian determinants of Q-functions. As a check for the new equations, we reproduce the numerical results for the Konishi operator previously obtained from the original infinite Y-system.

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Wrapping corrections beyond the 𝔰𝔩(2) sector in 𝒩 = 4 SYM

Beccaria

Macorini²,

Ratti

2012

Fortschritte der Physik

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The 𝔰𝔩(2) sector of 𝒩 = 4 SYM theory has been much studied and the anomalous dimensions of those operators are well known. Nevertheless, many interesting operators are not included in this sector. We consider a class of twist operators beyond the 𝔰𝔩(2) subsector introduced by Freyhult, Rej and Zieme. They are spin n, length‐3 operators. At one‐loop they can be identified with three gluon operators. At strong coupling, they are associated with spinning strings with two spins in AdS space and charge in S5. We exploit the Y‐system to compute the leading weak‐coupling four loop wrapping correction to their anomalous dimension. The result is written in closed form as a function of the spin n. We combine the wrapping correction with the known four loop asymptotic Bethe Ansatz contribution and analyze special limits in the spin n. In particular, at large n, we prove that a generalized Gribov‐Lipatov reciprocity holds. At negative unphysical spin, we present a simple BFKL‐like equation predicting the rightmost leading poles.

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Supersymmetric Bethe ansatz and Baxter equations from discrete Hirota dynamics

Cited by 133 publications

References 60 publications

Quantum spectral curve for arbitrary state/operator in AdS5/CFT4

Quantum spectral curve for arbitrary state/operator in AdS5/CFT4

Solving the AdS/CFT Y-system

Wrapping corrections beyond the 𝔰𝔩(2) sector in 𝒩 = 4 SYM

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