Integrability and the AdS/CFT correspondence

Rej, Adam

doi:10.1088/1751-8113/42/25/254002

Cited by 13 publications

(21 citation statements)

References 126 publications

(348 reference statements)

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“…We further assume that the "fat" string is not much disturbed by the insertion of the "slim" vertex operator, which means that two of the operators in the correlator must be virtually the same. 4 Then we only need to know the fat-string solution for the two-point function and the vertex operator of the slim string.…”

Section: Jhep09(2010)030mentioning

confidence: 99%

“…On the other hand, the spinning string solutions with non-zero angular momenta in AdS approach the boundary at a point only if the worldsheet is Minkowskian [17], otherwise (in the Euclidean signature) the boundary maps to a line [18,26]. 4 More precisely, they should be conjugate.…”

Section: General Formalismmentioning

confidence: 99%

“…4) where cos θ is the leading-order solution (A.2). There are two possible regimes: (I) τ → ∞, finite χ and (II) τ → ∞, χ → 0, χτ -fixed.…”

Section: A Spike In Smentioning

confidence: 99%

“…The two-point functions, by conformal symmetry, are determined by the spectrum of anomalous dimensions, which can be computed non-perturbatively with the help of integrability (see [4][5][6] for recent reviews), in the leading planar order of the large-N expansion. The threepoint functions are the simplest observables of the next order in 1/N .…”

Section: Introductionmentioning

confidence: 99%

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Holographic three-point functions of semiclassical states

Zarembo

2010

J. High Energ. Phys.

125

266

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Section: Jhep09(2010)030mentioning

confidence: 99%

Section: General Formalismmentioning

confidence: 99%

“…4) where cos θ is the leading-order solution (A.2). There are two possible regimes: (I) τ → ∞, finite χ and (II) τ → ∞, χ → 0, χτ -fixed.…”

Section: A Spike In Smentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Holographic three-point functions of semiclassical states

Zarembo

2010

J. High Energ. Phys.

125

266

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“…As in this section we do not present new results, we refer the reader to the reviews [137,9] for some background on the AdS/CFT correspondence, and [138,139,140,9] for some general background on string theory. Integrability in the AdS/CFT correspondence has been reviewed in [24,141,142,143,111] 4.1. String theory on AdS 5 × S 5…”

Section: The Ads/cft Correspondencementioning

confidence: 99%

Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities

Spill

2012

Rev. Math. Phys.

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In the following paper, which is based on the authors PhD thesis submitted to Imperial College London, we explore the applicability of Yangian symmetry to various integrable models, in particular, in relation with S-matrices. One of the main themes in this work is that, after a careful study of the mathematics of the symmetry algebras one finds that in an integrable model, one can directly reconstruct S-matrices just from the algebra. It has been known for a long time that S-matrices in integrable models are fixed by symmetry. However, Lie algebra symmetry, the Yang-Baxter equation, crossing and unitarity, which are what constrains the S-matrix in integrable models, are often taken to be separate, independent properties of the S-matrix. Here, we construct scattering matrices purely from the Yangian, showing that the Yangian is the right algebraic object to unify all required symmetries of many integrable models. In particular, we reconstruct the Smatrix of the principal chiral field, and, up to a CDD factor, of other integrable field theories with su(n) symmetry. Furthermore, we study the AdS/CFT correspondence, which is also believed to be integrable in the planar limit. We reconstruct the S-matrices at weak and at strong coupling from the Yangian or its classical limit. We give a pedagogical introduction into the subject, presenting a unified perspective of Yangians and their applications in physics. This paper should hence be accessible to mathematicians who would like to explore the application of algebraic objects to physics as well as to physicists interested in a deeper understanding of the mathematical origin of physical quantities.Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities 7 mensional symmetry algebras extending traditional Lie algebras. Indeed, they can be considered as deformations of the universal enveloping algebra of g [u], which is the algebra of polynomials in u with values in a simple Lie algebra g. The original definition of Yangians was given in [48], where the algebraic structure behind rational solutions to the Yang-Baxter equation was investigated. It is named after C.N. Yang, who found the first rational R-matrix with su(n) invariance as given above. If one thinks of scattering problems, the parameter u will be related to the rapidity of the particles. An important property of Yangians is that they allow for a so-called quantum double construction [49]. On the classical level, this "doubles" the polynomial algebra g[u] to the loop algebra g[[u, u −1 ]]. The importance of this construction lies in the fact that these quantum doubles have a universal R-matrix, which is an R-matrix defined in terms of the abstract generators of the Yangian Double. It satisfies an abstract Yang-Baxter equation, and is inverted by the action of the antipode map. Upon specifying a representation, this universal R-matrix should automatically lead to crossing invariant solutions of the Yang-Baxter equation. One problem is that simple evaluation representations, which enable one to...

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