Hagedorn Temperature of 
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 via Integrability

Harmark, Troels; Wilhelm, Matthias

doi:10.1103/physrevlett.120.071605

Cited by 27 publications

(65 citation statements)

References 37 publications

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“…• In [77,78] a modified version of the QSC was used to efficiently compute the Hagedorn temperature in N = 4 SYM in various regimes. The connection to QSC was found by reformulating the problem in a TBA language.…”

Section: Highlights Of Qsc-based Resultsmentioning

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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Section: Highlights Of Qsc-based Resultsmentioning

confidence: 99%

A review of the AdS/CFT Quantum Spectral Curve

Levkovich-Maslyuk¹

2020

J. Phys. A: Math. Theor.

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“…Asymptotic behavior We can infer the asymptotic behavior of P a (u) and Q i (u) at large spectral parameter u from the asymptotic behavior of the Y-functions found in Ref. [1]. At large u, the Y-functions asymptote to constants determined from a one-parameter family of constant T-systems with parameter z, see Eqs.…”

Section: Qsc Equations For the Hagedorn Temperaturementioning

confidence: 86%

“…[7,8] for reviews. Recently, we proposed a framework for calculating the Hagedorn temperature of AdS 5 /CFT 4 using integrability [1]. In this Letter, we take this a step further by exploiting this connection to compute the Hagedorn temperature at finite 't Hooft coupling.…”

Section: Introductionmentioning

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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“…This shows that these single string states have the Hagedorn behavior: the entropy is proportional to the energy. Indeed, the Hagedorn temperature has been computed via integrability in [32,33] We want to analyze these configurations further. For that we need to think about varyingλ, from small values to large values.…”

Section: The Small Black Hole In Ads and Phase Separation On The Spherementioning

confidence: 99%