Open fishchain in N = 4 Supersymmetric Yang-Mills Theory

Gromov, Nikolay; Julius, Julius; Primi, Nicolò

doi:10.1007/jhep07(2021)127

Cited by 15 publications

(15 citation statements)

References 83 publications

(158 reference statements)

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“…A recent important advance was the adaptation of the QSC to describe the spectrum of the defect CFT in the planar limit [40,48,49]. The approach we started in [24] is to exploit the knowledge of the exact spectrum to extract maximal information from the NCB.…”

Section: Discussionmentioning

confidence: 99%

Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds

Cavaglià,

Gromov,

Julius

et al. 2022

Preprint

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We continue to develop Bootstrability -a method merging Integrability and Conformal Bootstrap to extract CFT data in integrable conformal gauge theories such as N =4 SYM. In this paper, we consider the 1D defect CFT defined on a 1 2 -BPS Wilson line in the theory, whose non-perturbative spectrum is governed by the Quantum Spectral Curve (QSC). In addition, we use that the deformed setup of a cusped Wilson line is also controlled by the QSC. In terms of the defect CFT, this translates into two nontrivial relations connecting integrated 4-point correlators to cusp spectral data, such as the Bremsstrahlung and Curvature functions -known analytically from the QSC. Combining these new constraints and the spectrum of the 10 lowest-lying states with the Numerical Conformal Bootstrap, we obtain very sharp rigorous numerical bounds for the structure constant of the first nonprotected state, giving this observable with seven digits precision for the 't Hooft coupling in the intermediate coupling region4π ∼ 1, with the error decreasing quickly at large 't Hooft coupling. Furthermore, for the same structure constant we obtain a 4-loop analytic result at weak coupling. We also present results for excited states.

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Section: Discussionmentioning

confidence: 99%

Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds

Cavaglià,

Gromov,

Julius

et al. 2022

Preprint

Self Cite

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show abstract

“…Nevertheless the functional scalar product approach to overlaps and correlators was recently developed [243] and would be very instructive to match it with an explicit diagonalisation of the B operator to single out the natural basis of Q-functions. In a similar manner to the closed AdS 5 fishchain mentioned above an open fishchain has also been constructed [244] to describe cusped Wilson loops in a certain ladders limit of Feynman diagrams. This warrants the further development of separation of variables for open integrable systems with high-rank symmetry which has recently been analysed in [245].…”

Section: Discussionmentioning

confidence: 99%

Integrable systems, separation of variables and the Yang-Baxter equation

Ryan¹

2022

Preprint

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This article, based on the author's PhD thesis, reviews recent advancements in the field of quantum integrability, in particular the separation of variables (SoV) program for high-rank integrable spin chains and the boost mechanism for solving the Yang-Baxter equation. We begin with a general overview of quantum integrable systems with special emphasis on their description in terms of quantum algebras. We then provide a detailed account of the Yangian Y(gl(n)) of gl(n) in particular the Bethe algebra, fusion and T-and Q-systems. We then introduce the notion of separation of variables in integrable systems and build on Sklyanin's work in rank 1 models and extend to higher rank. By exploiting a novel link between SoV and quantum algebra representation theory we construct the separated variables for high-rank gl(n) bosonic spin chains for arbitrary compact representations of the symmetry algebra and develop various new tools along the way. Next, we build on the previous part and develop a new technique for the computation of scalar products in the SoV framework which we call Functional SoV or FSoV. Unlike the work in the previous part, which was operatorial, this approach is functional and is based on the Baxter TQ equations. After developing this technique we supplement it with a new operator construction providing a unified view of functional and operatorial SoV. Then, we generalise the results of the previous part from compact spin chains to non-compact spin chains.The final part of this work is based on the development of tools for solving the Yang-Baxter equation. We develop a bottom-up approach for this based on the so-called Boost automorphism and uses the spin chain Hamiltonian as a starting point. Our approach allows us to classify numerous families of solutions in particular a complete classification of 4 × 4 solutions which preserve fermion number which have applications in the AdS/CFT correspondence.

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“…As well as this the SoV construction for models with open boundary conditions has recently been studied [55] with operatorial methods. Such a spin chain is known to describe a Wilson loop in N " 4 SYM with insertions of local operators in the ladders limit [56].…”

Section: Discussionmentioning

confidence: 99%

Form-factors and complete basis of observables via separation of variables for higher rank spin chains

Gromov¹,

Primi²,

Ryan³

2022

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Integrable slpN q spin chains, which we consider in this paper, are not only the prototypical example of quantum integrable systems but also systems with a wide range of applications. For these models we use the Functional Separation of Variables (FSoV) technique with a new tool called Character Projection to compute all matrix elements of a complete set of operators, which we call principal operators, in the basis diagonalising the tower of conserved charges as determinants in Q-functions. Building up on these results we then derive similar determinant forms for the form-factors of combinations of multiple principal operators between arbitrary factorizable states, which include, in particular, off-shell Bethe vectors and Bethe vectors with arbitrary twists. We prove that the set of principal operators generates the complete spin chain Yangian. Furthermore, we derive the representation of these operators in the SoV bases allowing one to compute correlation functions with an arbitrary number of principal operators. Finally, we show that the available combinations of multiple insertions includes Sklyanin's SoV B operator. As a result, we are able to derive the B operator for slpN q spin chains using a minimal set of ingredients, namely the FSoV method and the structure of the SoV basis.

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Open fishchain in N = 4 Supersymmetric Yang-Mills Theory

Cited by 15 publications

References 83 publications

Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds

Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds

Integrable systems, separation of variables and the Yang-Baxter equation

Form-factors and complete basis of observables via separation of variables for higher rank spin chains

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