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, 809

"... Structure of large spin expansion of anomalous dimensions ..."

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### Imperial-TP-AT-2008-4 Structure of large spin expansion of anomalous dimensions at strong coupling

, 809

"... The anomalous dimensions of planar N = 4 SYM theory operators like tr(ΦD S +Φ) expanded in large spin S have the asymptotics γ = f lnS + fc + 1 S (f11 lnS + f10) +..., where f (the universal scaling function or cusp anomaly), fc and fmn are given by power series in the ‘t Hooft coupling λ. The suble ..."

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The anomalous dimensions of planar N = 4 SYM theory operators like tr(ΦD S +Φ) expanded in large spin S have the asymptotics γ = f lnS + fc + 1 S (f11 lnS + f10) +..., where f (the universal scaling function or cusp anomaly), fc and fmn are given by power series in the ‘t Hooft coupling λ. The subleading coefficients appear to be related by the so called functional relation and parity (reciprocity) property of the function expressing γ in terms of the conformal spin of the collinear group. Here we study the structure of such large spin expansion at strong coupling via AdS/CFT, i.e. by using the dual description in terms of folded spinning string in AdS5. The large spin expansion of the classical string energy happens to have exactly the same structure as that of γ in the perturbative gauge theory. Moreover, the functional relation and the reciprocity constraints on the coefficients are also satisfied. We compute the leading string 1-loop corrections to the coefficients fc, f11, f10 and verify the functional/reciprocity relations at subleading 1 √ λ order. This provides a strong indication that these relations hold not only in weak coupling (gauge-theory) but also in strong coupling (string-theory) perturbative expansions.

### unknown title

, 806

"... 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 the ..."

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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. 1 Wilson operator product expansions (OPE) [1] are the main tools in analyses of light-cone dominated processes, with deeply inelastic scattering being the most prominent representative.

### overview article: arxiv:1012.3982 Review of AdS/CFT Integrability, Chapter III.4: Twist states and the cusp anomalous dimension

"... Abstract: We review the computation of the anomalous dimension of twist operators in the planar limit of N = 4 SYM using the asymptotic Bethe ansatz and demonstrate how this quantity is obtained at weak, strong and intermediate values of the coupling constant. The anomalous dimension of twist operat ..."

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Abstract: We review the computation of the anomalous dimension of twist operators in the planar limit of N = 4 SYM using the asymptotic Bethe ansatz and demonstrate how this quantity is obtained at weak, strong and intermediate values of the coupling constant. The anomalous dimension of twist operators in the limit of large Lorentz spin played a major role in the construction as well as in many tests of the asymptotic Bethe equations, this aspect of the story is emphasised. ar X iv

### J H E P03(2009)129 Published by IOP Publishing for SISSA

, 2009

"... Abstract: We present a formula for the five-loop anomalous dimension of N = 4 SYM twist-three operators in the sl(2) sector. We obtain its asymptotic part from the Bethe Ansatz and finite volume corrections from the generalized Lüscher formalism, considering scattering processes of spin chain magno ..."

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Abstract: We present a formula for the five-loop anomalous dimension of N = 4 SYM twist-three operators in the sl(2) sector. We obtain its asymptotic part from the Bethe Ansatz and finite volume corrections from the generalized Lüscher formalism, considering scattering processes of spin chain magnons with virtual particles that travel along the cylinder. The complete result respects the expected large spin scaling properties and passes non-trivial tests including reciprocity constraints. We analyze the pole structure and find agreement with a conjectured resummation formula. In analogy with the twist-two anomalous dimension at four-loops wrapping effects are of order (log2M/M2) for large values of the spin.