Lüscher formula for GKP string

Basso, Benjamin; Belitsky, Andrei

doi:10.1016/j.nuclphysb.2012.02.011

Cited by 26 publications

(82 citation statements)

References 130 publications

(495 reference statements)

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“…Summing these up, together with the O(1/k) term emerging from the expansion of the central charge (2.8), one gets This result, obtained here by resummation of conformal perturbation series, is in agreement with the result of Ref. [52] derived from the large-N study of the O(N ) nonlinear sigma model [53,54]. The expression of the effective central charge and, as a consequence, of the anomalous dimension of the twist field can be cast in the form of the expansion in terms of inverse 't Hooft constant λ by means of its relation to the O(3) coupling g, g 2 = 1/(2 √ λ).…”

Section: Twist Operators and Effective Central Chargesupporting

confidence: 91%

Twisting perturbed parafermions

Belitsky

2017

Physics Letters B

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The near-collinear expansion of scattering amplitudes in maximally supersymmetric Yang-Mills theory at strong coupling is governed by the dynamics of stings propagating on the five sphere. The pentagon transitions in the operator product expansion which systematize the series get reformulated in terms of matrix elements of branch-point twist operators in the two-dimensional O(6) nonlinear sigma model. The facts that the latter is an asymptotically free field theory and that there exists no local realization of twist fields prevents one from explicit calculation of their scaling dimensions and operator product expansion coefficients. This complication is bypassed making use of the equivalence of the sigma model to the infinite-level limit of WZNW models perturbed by current-current interactions, such that one can use conformal symmetry and conformal perturbation theory for systematic calculations. Presently, to set up the formalism, we consider the O(3) sigma model which is reformulated as perturbed parafermions.Comment: 16 pages, 4 figure

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Section: Twist Operators and Effective Central Chargesupporting

confidence: 91%

Twisting perturbed parafermions

Belitsky

2017

Physics Letters B

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“…At finite coupling, the pole at u = ia/2 is replaced by a square-root branch cut between ±2g + ia/2, and the recipe is to integrate u closely around this cut. Equivalently, we may bring the contour through the cut to the so-called Goldstone sheet [22,41], where the flux-tube ingredients greatly simplify, as we discuss next.…”

Section: Pentagon Opementioning

confidence: 99%

Origin of the Six-Gluon Amplitude in Planar N=4 Supersymmetric Yang-Mills Theory

2020

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We study the maximally-helicity-violating (MHV) six-gluon scattering amplitude in planar N = 4 super-Yang-Mills theory at finite coupling when all three cross ratios are small. It exhibits a double logarithmic scaling in the cross ratios, controlled by a handful of "anomalous dimensions" that are functions of the coupling constant alone. Inspired by known seven-loop results at weak coupling and the integrability-based pentagon OPE, we present conjectures for the all-order resummation of these anomalous dimensions. At strong coupling, our predictions agree perfectly with the string theory analysis. Intriguingly, the simplest of these anomalous dimensions coincides with one describing the light-like limit of the octagon, namely the four-point function of large-charge BPS operators. arXiv:2001.05460v1 [hep-th]

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“…Each insertion corresponds to an elementary excitation above the ground state. The spectrum of elementary excitations can be found exactly [8,9] by solving the Bethe-ansatz equations [6], and should agree at strong coupling with the spectrum of the string in light-cone gauge. A detailed comparison reveals, however, several mismatches [10].…”

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Fine structure of the string spectrum in AdS 5 × S 5

Zarembo

Zieme

2012

Jetp Lett.

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The spectrum of an infinite spinning string in AdS5 does not precisely match the spectrum of dual gauge theory operators, interpolated to the strong coupling regime with the help of Bethe-ansatz equations. We show that the mismatch is due to interactions in the string σ-model which cannot be neglected even at asymptotically large 't Hooft coupling. PACS numbers: Valid PACS appear hereAccording to the AdS/CFT correspondence [1][2][3], N = 4 supersymmetric Yang-Mills theory (SYM) and string theory in AdS 5 × S 5 have a common spectrum that continuously interpolates between the loop-corrected dimensional analysis at weak coupling and the string oscillator spectrum at strong coupling. The complete integrability of the AdS/CFT system makes the non-perturbative interpolation amenable to an exact description by methods of Bethe ansatz [4]. The string interpretation of the spectrum, however, is quite subtle and our goal is to find a potential resolution of these subtleties.We shall concentrate on a specific set of states related to twist-two operators tr ZD S + Z. Here Z is a complex scalar field in SYM and D + is the covariant derivative in light-cone direction. The twist operators constitute presumably the most studied sector of the SYM spectrum [5]. Their anomalous dimensions scale logarithmically with spin: ∆ S (λ) − S 2Γ cusp (λ) ln S, where the cusp anomalous dimension Γ cusp (λ) is a non-trivial function of the 't Hooft coupling λ = g 2 YM N , which can be computed non-perturbatively with the help of the Betheansatz equations [6]. On the string side, twist operators are described by a string spinning in the Anti-de-Sitter space [7]. When the spin is very large, the string becomes essentially infinite, extending all the way to the boundary. The energy density of this long string is equal to the cusp anomalous dimensions Γ cusp (λ).We will be interested in the spectrum of small fluctuations on top of the long string, which are dual to operators with extra field insertions, schematically:where Ψ i can be a field strength, a fermion or a scalar. Each insertion corresponds to an elementary excitation above the ground state. The spectrum of elementary excitations can be found exactly [8,9] by solving the Bethe-ansatz equations [6], and should agree at strong coupling with the spectrum of the string in light-cone gauge. A detailed comparison reveals, however, several mismatches [10]. Since the above operators have many uses, for instance they govern the collinear limits of scattering amplitudes [11], it is important to understand how these discrepancies are resolved.The string oscillation modes in light-cone gauge are two-dimensional massive particles, whose interactions are The fermions form four 2d Dirac spinors with eight degrees of freedom on shell. The SYM spectrum, continued to strong coupling, consists of [8]:(Field strength) (2) :Fermions (8) :where in brackets we indicated the number of degrees of freedom of each excitation. The agreement holds literally only for fermions. The heavy boson from AdS 3 is absent i...

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Lüscher formula for GKP string

Cited by 26 publications

References 130 publications

Twisting perturbed parafermions

Twisting perturbed parafermions

Origin of the Six-Gluon Amplitude in Planar N=4 Supersymmetric Yang-Mills Theory

Fine structure of the string spectrum in AdS 5 × S 5

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