From weak coupling to spinning strings

Freyhult, Lisa; Rej, Adam; Zieme, Stefan

doi:10.1007/jhep02(2010)050

Cited by 11 publications

(46 citation statements)

References 73 publications

(118 reference statements)

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“…This is correct for the dispersion relation or the vacuum contribution to Y ℓ (u) but not for the two-to-two S-matrix of such excitations. There is no contradiction here with the findings of [67] where only the case of length 3 was treated, implying a single excitation on top of the vacuum for us. The only exception to what have just been said is the gauge field, ℓ = 1, where the mapping to the conformal spin chain with s = 3/2 is valid for any length (i.e., for any number of excitations for us).…”

Section: Mirror Kinematics and Double Wick Rotation Symmetrycontrasting

confidence: 51%

“…Introducing both of them into the game can be done by extending the previous considerations to higher-rank subsectors of the ABA system. The fermions can be unscrambled, for instance, from the sl(2|1) subsector, while the gauge fields require a more thorough in-depth analysis [67]. The complete list of excitations was studied in [48,49].…”

Section: Finite-size Correctionsmentioning

confidence: 99%

“…Last but not least, the gauge field excitations and bound states thereof, are embedded into the ABA equations in the form of stacks of strings [67], The details of this embedding are recalled in Appendix B. By applying the fusion method to these complex solutions, we obtain the following representation for the function Y ℓ (u) associated to a bound state of ℓ gauge fields,…”

Section: Gauge Field and Bound Statesmentioning

confidence: 99%

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Lüscher formula for GKP string

Basso

Belitsky

2012

Nuclear Physics B

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We investigate finite-size corrections to anomalous dimensions of large-spin twist-two operators in the planar maximally supersymmetric Yang-Mills theory. We develop a framework for analysis of these corrections, that is complementary to the conventional spin-chain approach, by making use of the hole rather than the magnon picture. From the dual string theory perspective where the large-spin operator is identified with the Gubser-Klebanov-Polyakov (GKP) string, our approach is equivalent to constructing the first Lüscher correction to the energy of the GKP string by incorporating the contribution of virtual excitations propagating on it. It allows us to propose a formula that controls a particular class of large-spin corrections to the twist-two anomalous dimension and holds at any value of the coupling constant. Compared to wrapping corrections computed with magnons propagating on the spin chain, the finite-size corrections that are encoded in our formalism start at a lower loop level. Our formalism thus calls for modification of the asymptotic contributions which are conventionally incorporated within the Asymptotic Bethe Ansatz. An educated guess allows us to remedy this pitfall and successfully confront our predictions with known results up to five loop accuracy at weak coupling. Finally, our formula sheds light on the weak-to-strong coupling transition for the subleading large-spin corrections under study and confirms stringy expectations at strong coupling where they are found to be identical to the first Lüscher correction to the vacuum energy of the O(6) sigma model. *

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Section: Mirror Kinematics and Double Wick Rotation Symmetrycontrasting

confidence: 51%

Section: Finite-size Correctionsmentioning

confidence: 99%

Section: Gauge Field and Bound Statesmentioning

confidence: 99%

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Lüscher formula for GKP string

Basso

Belitsky

2012

Nuclear Physics B

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“…Along this line, the one-particle dispersion relations of the excitations (1.5) have been receiving much attention in the different coupling regimes (cf. for instance [19] and references therein); but recently they have been summarised, corrected and put forward in an illuminating work by Basso [20] (also reference therein).…”

mentioning

confidence: 99%

Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: Scattering, particles and minimal area Wilson loops

2015

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Moving from Beisert-Staudacher equations, the complete set of Asymptotic Bethe Ansatz equations and S-matrix for the excitations over the GKP vacuum is found. The resulting model on this new vacuum is an integrable spin chain of length R = 2 ln s (s = spin) with particle rapidities as inhomogeneities, two (purely transmitting) defects and SU (4) (residual R-)symmetry. The non-trivial dynamics of N = 4 SYM appears in elaborated dressing factors of the 2D two-particle scattering factors, all depending on the 'fundamental' one between two scalar excitations. From scattering factors we determine bound states. In particular, we study the strong coupling limit, in the non-perturbative, perturbative and giant hole regimes. Eventually, from these scattering data we construct the 4D pentagon transition amplitudes (perturbative regime). In this manner, we detail the multi-particle contributions (flux tube) to the MHV gluon scattering amplitudes/Wilson loops (OPE or BSV series) and re-sum them to the Thermodynamic Bubble Ansatz. *

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“…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].…”

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confidence: 99%

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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From weak coupling to spinning strings

Cited by 11 publications

References 73 publications

Lüscher formula for GKP string

Lüscher formula for GKP string

Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: Scattering, particles and minimal area Wilson loops

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

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