Separation of variables and scalar products at any rank

Cavaglià, Andrea; Gromov, Nikolay; Levkovich-Maslyuk, Fedor

doi:10.1007/jhep09(2019)052

Cited by 49 publications

(114 citation statements)

References 78 publications

(136 reference statements)

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“…We found the quantum Baxter TQrelations, which together with the quantization condition [7,8], give us direct access to the quantum spectrum of the model in complete generality. 15 This also opens ways to the separation of variables (SoV) construction, along the lines of the recent works [24][25][26][27].…”

Section: Resultsmentioning

confidence: 92%

The holographic dual of strongly γ-deformed $$ \mathcal{N} $$ = 4 SYM theory: derivation, generalization, integrability and discrete reparametrization symmetry

Gromov

Sever

2020

J. High Energ. Phys.

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Recently, we constructed the first-principle derivation of the holographic dual of N = 4 SYM in the double-scaled γ-deformed limit directly from the CFT side. The dual fishchain model is a novel integrable chain of particles in AdS 5 . It can be viewed as a discretized string and revives earlier string-bit approaches. The original derivation was restricted to the operators built out of one of two types of scalar fields. In this paper, we extend our results to the general operators having any number of scalars of both types, except for a very special case when their numbers are equal. Interestingly, the extended model reveals a new discrete reparametrization symmetry of the "world-sheet", preserving all integrals of motion. We use integrability to formulate a closed system of equations, which allows us to solve for the spectrum of the model in full generality, and present non-perturbative numerical results. We show that our results are in agreement with the Asymptotic Bethe Ansatz of the fishnet model up to the wrapping order at weak coupling.

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Section: Resultsmentioning

confidence: 92%

The holographic dual of strongly γ-deformed $$ \mathcal{N} $$ = 4 SYM theory: derivation, generalization, integrability and discrete reparametrization symmetry

Gromov

Sever

2020

J. High Energ. Phys.

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“…Another reason why Q-functions with more than one index are important is that they appear to play a key role in the separation of variables for higher rank models, as observed recently in[41].…”

mentioning

confidence: 85%

“…Recently similar techniques were developed for non-compact spin chains in [41], extending the Sklyanin scalar product in SoV beyond simplest gl(2)-type models.…”

Section: From the Qsc To Correlators: Examplementioning

confidence: 99%

A review of the AdS/CFT Quantum Spectral Curve

Levkovich-Maslyuk¹

2020

J. Phys. A: Math. Theor.

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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. To appear in a special issue of J. Phys. A based on lectures given at the Young Researchers Integrability School and Workshop 2018. * We will not present the original derivation of the QSC from other approaches such as TBA [29], since it is rather technical and in any case applies only for some subsets of states (for which the TBA is well understood). Instead we will present the final result and describe its algebraic structure, starting from simpler spin chains as a motivating example.

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“…However one can alternatively arrive at the same expression by following our argument as we show in appendix C; namely by rewriting the SoV integral for the norm [71] and factorizing it into two pieces. Such a trick would be useful for guessing the integral representation for the overlaps in higher-rank spin chains, for which the SoV integrals for the norms were discussed in [72,73].…”

Section: Jhep09(2020)180mentioning

confidence: 99%

Functional equations and separation of variables for exact g-function

Caetano

Komatsu

2020

J. High Energ. Phys.

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The g-function is a measure of degrees of freedom associated to a boundary of two-dimensional quantum field theories. In integrable theories, it can be computed exactly in a form of the Fredholm determinant, but it is often hard to evaluate numerically. In this paper, we derive functional equations — or equivalently integral equations of the thermodynamic Bethe ansatz (TBA) type — which directly compute the g-function in the simplest integrable theory; the sinh-Gordon theory at the self-dual point. The derivation is based on the classic result by Tracy and Widom on the relation between Fredholm determinants and TBA, which was used also in the context of topological string. We demonstrate the efficiency of our formulation through the numerical computation and compare the results in the UV limit with the Liouville CFT. As a side result, we present multiple integrals of Q-functions which we conjecture to describe a universal part of the g-function, and discuss its implication to integrable spin chains.

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Separation of variables and scalar products at any rank

Cited by 49 publications

References 78 publications

The holographic dual of strongly γ-deformed $$ \mathcal{N} $$ = 4 SYM theory: derivation, generalization, integrability and discrete reparametrization symmetry

The holographic dual of strongly γ-deformed $$ \mathcal{N} $$ = 4 SYM theory: derivation, generalization, integrability and discrete reparametrization symmetry

A review of the AdS/CFT Quantum Spectral Curve

Functional equations and separation of variables for exact g-function

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