Exact Three-Point Functions of Determinant Operators in Planar 
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 Supersymmetric Yang-Mills Theory

Jiang, Yunfeng; Komatsu, Shota; Vescovi, Edoardo

doi:10.1103/physrevlett.123.191601

Cited by 71 publications

(75 citation statements)

References 32 publications

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“…Note that a similar kernel played a key role in the recent study on the diagonal finite volume form factor in the sinh-Gordon model [145], which is based on the hidden Grassmann structure [146] and generalizes earlier results for the ground state [147]. One can bring our results to a form closer to theirs by first performing the integral convolution and reducing it to a finite-dimensional determinant [148].…”

Section: Jhep07(2020)037supporting

confidence: 68%

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Structure constants in $$ \mathcal{N} $$ = 4 SYM at finite coupling as worldsheet g-function

Jiang

Komatsu

Vescovi

2020

J. High Energ. Phys.

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173

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We develop a novel nonperturbative approach to a class of three-point functions in planar N = 4 SYM based on Thermodynamic Bethe Ansatz (TBA). More specifically, we study three-point functions of a non-BPS single-trace operator and two determinant operators dual to maximal Giant Graviton D-branes in AdS 5 ×S 5. They correspond to disk one-point functions on the worldsheet and admit a simpler and more powerful integrability description than the standard single-trace three-point functions. We first introduce two new methods to efficiently compute such correlators at weak coupling; one based on large N collective fields, which provides an example of open-closed-open duality discussed by Gopakumar, and the other based on combinatorics. The results so obtained exhibit a simple determinant structure and indicate that the correlator can be interpreted as a generalization of g-functions in 2d QFT; an overlap between an integrable boundary state and a state corresponding to the single-trace operator. We then determine the boundary state at finite coupling using the symmetry, the crossing equation and the boundary Yang-Baxter equation. With the resulting boundary state, we derive the ground-state g-function based on TBA and conjecture its generalization to other states. This is the first fully nonperturbative proposal for the structure constants of operators of finite length. The results are tested extensively at weak and strong couplings. Finally, we point out that determinant operators can provide better probes of sub-AdS locality than single-trace operators and discuss possible applications.

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Section: Jhep07(2020)037supporting

confidence: 68%

“…The derivation closely follows the one in appendix B of [244]. 148 The first step of rewriting is to factorize the matrix M and convert it to a sum of two matrices,…”

Section: R Q-functions and Overlap With Néel Statementioning

confidence: 99%

Structure constants in $$ \mathcal{N} $$ = 4 SYM at finite coupling as worldsheet g-function

Jiang

Komatsu

Vescovi

2020

J. High Energ. Phys.

Self Cite

173

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“…The reformulation of gluing conditions as a finiteness of norm discussed in sec 4.3 is also likely to uplift to full N = 4 SYM as suggested by derivation of the gluing conditions in [46]. Moreover, very recently some correlators of determinant operators were expressed in TBA language [107,108], suggesting again they may be fruitfully reformulated using the QSC. One may hope that if this program is successful, it would allow one to obtain correlation functions with the same precision and efficiency as the spectrum, and thus complete the solution of a 4d gauge theory for the first time.…”

Section: Resultsmentioning

confidence: 96%

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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“…More recently, it was found in [11,12] that a special class of three-point functions can be computed exactly using the techniques of the g-functions. The result is given in a closed form as the Fredholm determinant and is by far more compact and practical than the infinite series in the hexagon approach.…”

Section: Jhep09(2020)180mentioning

confidence: 99%

“…This streamlines the derivations and clarifies the origin of the simplicity of the final answer. As another extension, the "excited-state g-function"namely the overlap between the boundary state and an excited state -was discussed in [9] and a complete formula was written down in [11,12].…”

Section: Introductionmentioning

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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Exact Three-Point Functions of Determinant Operators in Planar N=4 Supersymmetric Yang-Mills Theory

Cited by 71 publications

References 32 publications

Structure constants in $$ \mathcal{N} $$ = 4 SYM at finite coupling as worldsheet g-function

Structure constants in $$ \mathcal{N} $$ = 4 SYM at finite coupling as worldsheet g-function

A review of the AdS/CFT Quantum Spectral Curve

Functional equations and separation of variables for exact g-function

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