Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1∣s+1)

Tsuboi, Zengo

doi:10.1016/s0378-4371(97)00625-0

Cited by 87 publications

(198 citation statements)

References 44 publications

(80 reference statements)

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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%

“…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%

“…The last one exchanges two indices of different types and usually is called fermionic QQ-relation [32,36]. They naturally appeared in the chain of Bäcklund transformations for the integrable Heisenberg gl(n|m) spin chains [32].…”

Section: Jhep09(2015)187mentioning

confidence: 99%

“…Assuming 33 Note that not all the roots of Y * 1,0 (u) + 1 give the Bethe roots. To identify correctly the right zeros one should follow them starting from the weak coupling limit, controlled by the ABA.…”

Section: Jhep09(2015)187mentioning

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.

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%

Section: Definition Of Q-system and Qq-relationsmentioning

confidence: 99%

Section: Jhep09(2015)187mentioning

confidence: 99%

Section: Jhep09(2015)187mentioning

confidence: 99%

See 2 more Smart Citations

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

Gromov

Казаков

Leurent

et al. 2015

J. High Energ. Phys.

193

519

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“…The procedure for fermionic duality on Bethe equations used in this section closely follows the general prescription discussed in [72][73][74][75]. The case at hand is very similar to the osp(6|4) spin-chain studied in [49,57].…”

Section: Fermionic Dualitymentioning

confidence: 99%

Integrability, spin-chains and the AdS3/CFT2 correspondence

Sax

Stefański

2011

J. High Energ. Phys.

146

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Building on arXiv:0912.1723 [1], in this paper we investigate the AdS 3 /CFT 2 correspondence using integrability techniques. We present an all-loop Bethe Ansatz (BA) for strings on AdS 3 × S 3 × S 3 × S 1 , with symmetry d(2, 1; α) 2 , valid for all values of α. This construction relies on a novel, α-dependent generalisation of the Zhukovsky map. We investigate the weakly-coupled limit of this BA and of the all-loop BA for strings on AdS 3 × S 3 × T 4 . We construct integrable short-range spin-chains and Hamiltonians that correspond to these weakly-coupled BAs. The spin-chains are alternating and homogenous, respectively. The alternating spinchain can be regarded as giving some of the first hints about the unknown CFT 2 dual to string theory on AdS 3 ×S 3 ×S 3 ×S 1 . We show that, in the α → 1 limit, the integrable structure of the d(2, 1; α) 2 model is non-singular and keeps track of not just massive but also massless modes. This provides a way of incorporating massless modes into the integrability machinery of the AdS 3 /CFT 2 correspondence.

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Hidden E-Type Structures in Dilute A Models

Suzuki

2000

Physical Combinatorics

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The hidden E 7 (E 6 ) structure has been conjectured for the minimal model M 4,5 (M 6,7 ) perturbed by Φ 1,2 in the context of conformal field theory(CFT). Motivated by this, we examine the dilute A 4,6 models, which are expected to be corresponding lattice models. Thermodynamics of the equivalent one dimensional quantum systems is analyzed via the quantum transfer matrix approach. Appropriate auxiliary functions, related to kinks in the theory, play a role in constructing functional relations among transfer matrices. We successfully recover the universal Y − systems and thereby Thermodynamic Bethe Ansatz equations for E 6,7 from the dilute A 6,4 model, respectively.

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Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1∣s+1)

Cited by 87 publications

References 44 publications

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

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

Integrability, spin-chains and the AdS3/CFT2 correspondence

Hidden E-Type Structures in Dilute A Models

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