Twist-three at five loops, Bethe ansatz and wrapping

Beccaria, Matteo; Форини, Валентина; Łukowski, Tomasz; Zieme, Stefan

doi:10.1088/1126-6708/2009/03/129

Cited by 59 publications

(82 citation statements)

References 72 publications

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“…Subsequently, the leading wrapping corrections for the lowest lying twist-three operators were also determined from Lüscher corrections [48]. These occur at 5-loop level.…”

Section: Weak Coupling Resultsmentioning

confidence: 99%

Review of AdS/CFT Integrability, Chapter III.5: Lüscher Corrections

Janik

2011

Lett Math Phys

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Abstract. In integrable quantum field theories, the large volume spectrum is given by the Bethe Ansatz. The leading corrections, due to virtual particles circulating around the cylinder, are encoded in so-called Lüscher corrections. In order to apply these techniques to the AdS/CFT correspondence, one has to generalize these corrections to the case of generic dispersion relations and to multiparticle states. We review these various generalizations and the applications of Lüscher's corrections to the study of the worldsheet QFT of the superstring in Ad S 5 × S 5 and, consequently, to anomalous dimensions of operators in N = 4 SYM theory.Mathematics Subject Classification (2010). 81T30, 81T40, 81U15, 81U20.

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“…Subsequently, the leading wrapping corrections for the lowest lying twist-three operators were also determined from Lüscher corrections [48]. These occur at 5-loop level.…”

Section: Weak Coupling Resultsmentioning

confidence: 99%

Review of AdS/CFT Integrability, Chapter III.5: Lüscher Corrections

Janik

2011

Lett Math Phys

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“…(2.19) 10 The counit and all other bialgebra structures are straightforwardly implemented, and do not present any novel features. 11 We use the conventions of [35].…”

Section: Jhep06(2010)033mentioning

confidence: 99%

“…On the one hand, a generalized Lüscher approach for treating the leading wrapping effects was developed [1][2][3][4][5][6][7][8][9][10][11][12][13] and successfully confronted against direct field-theoretic computations [14,15]. On the other hand, the Thermodynamic Bethe Ansatz based on the mirror theory [16] was advanced as a tool to capture the exact string spectrum in both the 't Hooft coupling constant λ and the size L of the system [17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

On Yangian and long representations of the centrally extended $ \mathfrak{s}\mathfrak{u}\left( {\left. 2 \right|2} \right) $ superalgebra

Arutyunov

Leeuw

Торриелли

2010

J. High Energ. Phys.

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The centrally extended su(2|2) superalgebra is an asymptotic symmetry of the light-cone string sigma model on AdS 5 × S 5 . We consider an evaluation representation of the conventional Yangian built over a particular 16-dimensional long representation of the centrally extended su(2|2). Interestingly, we find that S-matrices compatible with this evaluation representation do not exist. On the other hand, by requiring centrally extended su(2|2) invariance and explicitly solving the Yang-Baxter equation, we find a scattering matrix for long-short representations of the Lie superalgebra. We notice that this S-matrix is invariant under a different representation of non-evaluation type, induced from the tensor product of short representations. Our findings concern the conventional Yangian only, and are not applied to possible algebraic extensions of the latter.

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“…Beyond this order it is not known if or how the Bethe ansatz can be modified to incorporate these so-called wrapping interactions. For recent progress on the understanding of the wrapping problem in the special context of gauge/string duality see [21][22][23].…”

Section: Introduction and Overviewmentioning

confidence: 99%

Long-range deformations for integrable spin chains

Bargheer¹,

Beisert²,

Loebbert³

2009

J. Phys. A: Math. Theor.

200

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We present a recursion relation for the explicit construction of integrable spin chain Hamiltonians with long-range interactions. Based on arbitrary shortrange (e.g. nearest neighbor) integrable spin chains, it allows us to construct an infinite set of conserved long-range charges. We explain the moduli space of deformation parameters by different classes of generating operators. The rapidity map and dressing phase in the long-range Bethe equations are a result of these deformations. The closed chain asymptotic Bethe equations for long-range spin chains transforming under a generic symmetry algebra are derived. Notably, our construction applies to generalizations of standard nearest neighbor chains such as alternating spin chains. We also discuss relevant properties for its application to planar D = 4, N = 4 and D = 3, N = 6 supersymmetric gauge theories. Finally, we present a map between long-range and inhomogeneous spin chains delivering more insight into the structures of these models, as well as their limitations at wrapping order.

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Twist-three at five loops, Bethe ansatz and wrapping

Cited by 59 publications

References 72 publications

Review of AdS/CFT Integrability, Chapter III.5: Lüscher Corrections

Review of AdS/CFT Integrability, Chapter III.5: Lüscher Corrections

On Yangian and long representations of the centrally extended $ \mathfrak{s}\mathfrak{u}\left( {\left. 2 \right|2} \right) $ superalgebra

Long-range deformations for integrable spin chains

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