The scaling function at strong coupling from the quantum string Bethe equations

Beccaria, Matteo; Angelis, Gian Fabrizio De; Форини, Валентина

doi:10.1088/1126-6708/2007/04/066

Cited by 54 publications

(37 citation statements)

References 50 publications

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“…These coefficients were first predicted in [18] by the numerical analysis. In [19][20][21], the leading coefficient was computed analytically, and then, in [22], the expansion was systematically computed up to 1/g 40 . Of course, the strong coupling prediction (1.4) should be compared with the direct string worldsheet computation.…”

Section: Jhep09(2015)138mentioning

confidence: 99%

Resurgence of the cusp anomalous dimension

Dorigoni¹,

Hatsuda²

2015

J. High Energ. Phys.

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We revisit the strong coupling limit of the cusp anomalous dimension in planar N = 4 super Yang-Mills theory. It is known that the strong coupling expansion is asymptotic and non-Borel summable. As a consequence, the cusp anomalous dimension receives non-perturbative corrections, and the complete strong coupling expansion should be a resurgent transseries. We reveal that the perturbative and non-perturbative parts in the transseries are closely interrelated. Solving the Beisert-Eden-Staudacher equation systematically, we analyze in detail the large order behavior in the strong coupling perturbative expansion and show that the non-perturbative information is indeed encoded there. An ambiguity of (lateral) Borel resummations of the perturbative expansion is precisely canceled by the contributions from the non-perturbative sectors, and the final result is real and unambiguous.

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Section: Jhep09(2015)138mentioning

confidence: 99%

Resurgence of the cusp anomalous dimension

Dorigoni¹,

Hatsuda²

2015

J. High Energ. Phys.

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“…The perturbative solutions to the cusp equation were confirmed by field theoretical calculations to four-loop order in 't Hooft coupling [21], with the latter providing numerical confirmation for the conjectured all-order integrable structures in maximally supersymmetric gauge theory. Many attempts [35,36,37,38,39,40] to find a systematic strong coupling solution to the aforementioned equation culminated with the development of a scheme which allows one to develop inverse coupling expansion [41] (see also [42]). Due to the strong/weak nature of the AdS/CFT correspondence, this provides a prediction for the spectrum of corresponding string states.…”

Section: The Quasipartonic Operators O (ℓ)mentioning

confidence: 99%

Fine structure of anomalous dimensions inN=4super-Yang–Mills theory

Belitsky

Korchemsky²,

Pasechnik

2009

Nuclear Physics B

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Anomalous dimensions of high-twist Wilson operators in generic gauge theories occupy a band of width growing logarithmically with their conformal spin. We perform a systematic study of its fine structure in the autonomous SL(2) subsector of the dilatation operator of planar N = 4 superYang-Mills theory which is believed to be integrable to all orders in 't Hooft coupling. We resort in our study on the framework of the Baxter equation to unravel the properties of the ground state trajectory and the excited trajectories in the spectrum. We use two complimentary approaches in our analysis based on the asymptotic solution of the Baxter equation and on the semiclassical expansion to work out the leading asymptotic expression for the trajectories in the upper and lower part of the band and to find how they are modified by the perturbative corrections.

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“…The limit of the kernel K(u, u ′ ) is not uniform in u and one has to deal differently with different regions in the rapidity space u [78,212] . The leading term in (7.6) was first obtained numerically [71], and then analytically in [76,77,78,79]. The next term was obtained by Casteill and Kristjansen [80] and Belitsky [81], and the third term and a recursive procedure for the next terms by Basso, Korchemsky and Kotanski [82] and in [83].…”

Section: The Cusp Anomalous Dimensionmentioning

confidence: 99%

“…Analytical results were much more difficult to obtain. The first order was reproduced by a series of works [76,77,78,79], the next term was obtained by Casteill and Kristjansen [80] and Belitsky [81], and the third term and a recursive procedure for the next terms by Basso, Korchemsky and Kotanski [82] and in [83]. Another object extensively studied at strong coupling, from the point of view of the Bethe ansatz and the string theory, is the generalized scaling function which also appears in the study of the logarithmic scaling in the sl(2) sector of the theory.…”

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confidence: 99%

Integrability and the AdS/CFT correspondence

Serban¹

2011

J. Phys. A: Math. Theor.

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The description of gauge theories at strong coupling is one of the long-standing problems in theoretical physics. The idea of a relation between strongly coupled gauge theories and string theory was pioneered by 't Hooft, Wilson and Polyakov. A decade ago, Maldacena made this relation explicit by conjecturing the exact equivalence of a conformally invariant theory in four dimensions, the maximally supersymmetric Yang-Mills theory, with string theory in the AdS 5 × S 5 background. Other examples of correspondence between a conformally invariant theory and string theory in an AdS background were discovered recently. The comparison of the two sides of the correspondence requires the use of non-perturbative methods. The discovery of integrable structures in gauge theory and string theory led to the conjecture that the two theories are integrable for any value of the coupling constant and that they share the same integrable structure defined non-perturbatively. The last eight years brought remarkable progress in identifying this solvable model and in explicitly solving the problem of computing the spectrum of conformal dimensions of the theory. The progress came from the identification of the dilatation operator with an integrable spin chain and from the study of the string sigma model. In this thesis, I present the evolution of the concept of integrability in the framework of the AdS/CFT correspondence and the the main results obtained using this approach.

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The scaling function at strong coupling from the quantum string Bethe equations

Cited by 54 publications

References 50 publications

Resurgence of the cusp anomalous dimension

Resurgence of the cusp anomalous dimension

Fine structure of anomalous dimensions inN=4super-Yang–Mills theory

Integrability and the AdS/CFT correspondence

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