The full Quantum Spectral Curve for AdS4/CFT3

Bombardelli, Diego; Cavaglià, Andrea; Fioravanti, Davide; Gromov, Nikolay; Tateo, Roberto

doi:10.1007/jhep09(2017)140

Cited by 51 publications

(75 citation statements)

References 77 publications

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“…In the paper [14] a large variety of such graphs, relevant for the computations of anomalous dimensions, is described and some of these graphs are computed by the help of integrability. Similar double scaling limit has been observed in [14] for the ABJ(M) model, for which the QSC is also known [15,16]. In the ABJ(M) theory the Feynman graphs are dominated in the bulk by the regular rectangular "fishnet" lattice structure.…”

Section: Introductionsupporting

confidence: 75%

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Integrability of conformal fishnet theory

Gromov

Казаков

Korchemsky

et al. 2018

J. High Energ. Phys.

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115

245

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Abstract:We study integrability of fishnet-type Feynman graphs arising in planar fourdimensional bi-scalar chiral theory recently proposed in arXiv:1512.06704 as a special double scaling limit of gamma-deformed N = 4 SYM theory. We show that the transfer matrix "building" the fishnet graphs emerges from the R−matrix of non-compact conformal SU(2, 2) Heisenberg spin chain with spins belonging to principal series representations of the four-dimensional conformal group. We demonstrate explicitly a relationship between this integrable spin chain and the Quantum Spectral Curve (QSC) of N = 4 SYM. Using QSC and spin chain methods, we construct Baxter equation for Q−functions of the conformal spin chain needed for computation of the anomalous dimensions of operators of the type tr(φ J 1 ) where φ 1 is one of the two scalars of the theory. For J = 3 we derive from QSC a quantization condition that fixes the relevant solution of Baxter equation. The scaling dimensions of the operators only receive contributions from wheel-like graphs. We develop integrability techniques to compute the divergent part of these graphs and use it to present the weak coupling expansion of dimensions to very high orders. Then we apply our exact equations to calculate the anomalous dimensions with J = 3 to practically unlimited precision at any coupling. These equations also describe an infinite tower of local conformal 1 Unité Mixte de Recherche 3681 du CNRS.Open Access, c The Authors. Article funded by SCOAP 3 .https://doi.org/10.1007/JHEP01 (2018)095 JHEP01 (2018)095 operators all carrying the same charge J = 3. The method should be applicable for any J and, in principle, to any local operators of bi-scalar theory. We show that at strong coupling the scaling dimensions can be derived from semiclassical quantization of finite gap solutions describing an integrable system of noncompact SU(2, 2) spins. This bears similarities with the classical strings arising in the strongly coupled limit of N = 4 SYM.

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Section: Introductionsupporting

confidence: 75%

“…As a consequence, the four solutions to (3.6) have to satisfy 2nd order finite difference equations, e.g. 16) and the second equation is obtained by replacing ∆ → 4 − ∆. By matching the asymptotics (4.6), we find that Q 2 and Q 3 satisfy (4.16) whereas Q 1 and Q 4 satisfy the second equation.…”

Section: Double-scaling Limitmentioning

confidence: 91%

Integrability of conformal fishnet theory

Gromov

Казаков

Korchemsky

et al. 2018

J. High Energ. Phys.

Self Cite

115

245

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show abstract

“…• The QSC has been also formulated for the Hubbard model [60,61] and for the ABJM theory [62,63]. For ABJM it provided high-order perturbative results and very precise numerics [64,65,66,67,68], the latter confirming and extending a much older TBA calculation [69].…”

Section: Highlights Of Qsc-based Resultsmentioning

confidence: 68%

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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“…This could provide a connection to the cases of the Hagedorn temperature in the pp-wave or spin-matrix-theory limits [34][35][36][37][38][39][40][41][42][43]. Moreover, it would be interesting to consider the Hagedorn temperature for integrable deformations of N = 4 SYM theory (see [44] for one-loop results) and for the three-dimensional N = 6 superconformal Chern-Simons theory, for which a QSC formulation for the spectral problem exists as well [45]. In particular, it would be intriguing to study what happens at strong coupling in these cases.…”

Section: Discussionmentioning

confidence: 99%

The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve

Harmark¹,

Wilhelm²

2018

Physics Letters B

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Building on the recently established connection between the Hagedorn temperature and integrability [1], we show how the Quantum Spectral Curve formalism can be used to calculate the Hagedorn temperature of AdS5/CFT4 for any value of the 't Hooft coupling. We solve this finite system of finite-difference equations perturbatively at weak coupling and numerically at finite coupling. We confirm previous results at weak coupling and obtain the previously unknown three-loop Hagedorn temperature. Our finite-coupling results interpolate between weak and strong coupling and allow us to extract the first perturbative order at strong coupling. Our results indicate that the Hagedorn temperature for large 't Hooft coupling approaches that of type IIB string theory in ten-dimensional Minkowski space.

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The full Quantum Spectral Curve for AdS4/CFT3

Cited by 51 publications

References 77 publications

Integrability of conformal fishnet theory

Integrability of conformal fishnet theory

A review of the AdS/CFT Quantum Spectral Curve

The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve

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