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The Yangians, Bethe Ansatz and combinatorics

✍ Scribed by A. N. Kirillov; N. Yu. Reshetikhin

Publisher
Springer
Year
1986
Tongue
English
Weight
380 KB
Volume
12
Category
Article
ISSN
0377-9017

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✦ Synopsis

An axiomatic definition of a quantum monodromy matrix and the representations of its corresponding Hopf algebra are discussed. The connection between the quantum inverse transform method and the representation theory of a symmetric group is considered. A new approach to the completeness problem of Bethe vectors is also given.

πŸ“œ SIMILAR VOLUMES

Yangian symmetry, S-matrices and Bethe a
Yangian symmetry, S-matrices and Bethe ansatz for the AdS5 Γ— S5 superstring
✍ M. de Leeuw πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 184 KB

## Abstract We discuss the relation between the recently derived bound state S‐matrices for the AdS~5~Γ— S^5^ superstring and Yangian symmetry. We will study the relation between this Yangian symmetry and the Bethe ansatz. In particular we can use it to derive the Bethe equations for bound states.

Supersymmetric Vacua and Bethe Ansatz
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✍ Nikita A. Nekrasov; Samson L. Shatashvili πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 459 KB
Semiclassical Bethe ansatz and AdS/CFT
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✍ K. Zarembo πŸ“‚ Article πŸ“… 2005 πŸ› John Wiley and Sons 🌐 English βš– 189 KB

## Abstract The Bethe ansatz can be used to compute anomalous dimensions in 𝒩 = 4 SYM theory. The classical solutions of the sigma‐model on __AdS__^5^ Γ— __S__^5^ can also be parameterized by an integral equation of Bethe type. The relationship between the two Bethe ansΓ€tze is reviewed.