Algebra of transfer-matrices and Yang-Baxter equations on the string worldsheet in AdS(5) x S(5)

Details Algebra of transfer-matrices and Yang-Baxter equations on the string worldsheet in AdS(5) x S(5) Algebra of transfer-matrices and Yang-Baxter equations on the string worldsheet in AdS(5) x S(5)

2007-12-27

arxiv.org/abs/0712.4278v2

Nucl.Phys.B802:1-39,2008

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 47 pp; v2: clarified the relation to the calculation of Poisson bracket (Section 2.2.2); added example in Section 7

Scientific paper

10.1016/j.nuclphysb.2008.04.029

Integrability of the string worldsheet theory in AdS(5) x S(5) is related to the existence of a flat connection depending on the spectral parameter. The transfer matrix is the open-ended Wilson line of this flat connection. We study the product of transfer matrices in the near-flat space expansion of the AdS(5) x S(5) string theory in the pure spinor formalism. The natural operations on Wilson lines with insertions are described in terms of r- and s-matrices satisfying a generalized classical Yang-Baxter equation. The formalism is especially transparent for infinite or closed Wilson lines with simple gauge invariant insertions.

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