The Tetrahedron Zamolodchikov Algebra and the AdS5 x S5 S-matrix

Abstract

The S-matrix of the $Ad{S}_5\times S^5$ string theory is a tensor product of two centrally extended su(2|2) S-matrices, each of which is related to the R-matrix of the Hubbard model. The R-matrix of the Hubbard model was first found by Shastry, who ingeniously exploited the fact that, for zero coupling, the Hubbard model can be decomposed into two XX models. In this article, we review and clarify this construction from the AdS/CFT perspective and investigate the implications this has for the $Ad{S}_5\times S^5$ S-matrix.

41 pages, 1 table, revised version, published in Communications in Mathematical Physics (2017)

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Cited by in corpus (9)

• Integrability of the AdS_5 x S^5 superstring and its deformations
• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• Integrability treatment of AdS/CFT orbifolds
• On $Ad{S}_2/CF{T}_1$ transfer matrices, Bethe ansatz and scale invariance
• The Lax pair for the fermionic Bazhanov-Stroganov $R$-operator
• The tetrahedral Zamolodchikov algebra for the fermionic Bazhanov-Stroganov R-operator
• An Elliptic Parameterisation of the Zamolodchikov Model
• On extension of the Yang-Baxter equation and the fermionic $R$-operator
• On integrability of the one-dimensional Hubbard model