Weakly coupled 𝒩 = 4 Super Yang-Mills and 𝒩 = 6 Chern-Simons theories from u(2|2) Yangian symmetry

Spill, Fabian

doi:10.1088/1126-6708/2009/03/014

Cited by 18 publications

(13 citation statements)

References 40 publications

(54 reference statements)

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“…We plan to come back to this issue in the future, in the light of possible consequences for the abstract form of the universal R-matrix (cf. for instance [59,60]). …”

Section: The Classical Limitmentioning

confidence: 99%

The bound state S-matrix for superstring

2009

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Abstract:We determine the S-matrix that describes scattering of arbitrary bound states in the light-cone string theory in AdS 5 × S 5 . The corresponding construction relies on the Yangian symmetry and the superspace formalism for the bound state representations. The basic analytic structure supporting the S-matrix entries turns out to be the hypergeometric function 4 F 3 . We show that for particular bound state numbers it reproduces all the scattering matrices previously obtained in the literature. Our findings should be relevant for the TBA and Lüscher approaches to the finite-size spectral problem. They also shed some light on the construction of the universal R-matrix for the centrally-extended psu(2|2) superalgebra.

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“…We plan to come back to this issue in the future, in the light of possible consequences for the abstract form of the universal R-matrix (cf. for instance [59,60]). …”

Section: The Classical Limitmentioning

confidence: 99%

The bound state S-matrix for superstring

2009

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“…Furthermore, we derive the weak coupling S-matrix also from the Yangian. These results have been published in [94]. As we have established the mathematical machinery of universal R-matrices in chapter 2, we can obtain this S-matrix in a straightforward fashion.…”

Section: Outlinementioning

confidence: 92%

“…As we have studied the mathematics underlying the symmetries encountered in the AdS/CFT correspondence, the physics (in form of the S-matrix) follows straightforwardly. The results of section 5.2 have been ws-rmp Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities 91 published in [94], were an explicit derivation of the universal R-matrix of u(2|2) was done.…”

Section: The Magnon S-matrix Of Ads/cftmentioning

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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“…Integrability plays a key role in unveiling the structure of planar ABJM theory [7,8,9,10,11,12,13,14]. At leading order in the weak coupling expansion, it was proven that the spectrum of of anomalous dimensions for certain subsets of singletrace, gauge invariant operators of the theory is encoded in an integrable spin chain Hamiltonian [7,8,9], of the general form…”

Section: Introductionmentioning

confidence: 99%

Two-loop spectroscopy of short ABJM operators

Παπαθανασίου

Spradlin

2010

J. High Energ. Phys.

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We study the spectrum of anomalous dimensions of short operators in planar ABJM theory at two loops. Specifically we develop a method for solving the OSp(6|4) Bethe ansatz equations for a certain class of unpaired length-4 states with arbitrarily high number of excitations, and apply it to identify three new sequences of rational eigenvalues. Results for low-lying paired states in the OSp(4|2) sector are obtained by direct diagonalization of the spin chain Hamiltonian. We also study the SL(2|1) sector and identify the set of states that corresponds to the SL(2)-like Bethe ansatz of Gromov and Vieira. Finally we extend part of our analysis to length-6 operators.

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Weakly coupled 𝒩 = 4 Super Yang-Mills and 𝒩 = 6 Chern-Simons theories from u(2|2) Yangian symmetry

Cited by 18 publications

References 40 publications

The bound state S-matrix for superstring

The bound state S-matrix for superstring

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

Two-loop spectroscopy of short ABJM operators

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