Algebra of transfer-matrices and Yang-Baxter equations on the string worldsheet in AdS(5) x S(5)
arXiv:0712.4278 · doi:10.1016/j.nuclphysb.2008.04.029
Abstract
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.
LaTeX, 47 pp; v2: clarified the relation to the calculation of Poisson bracket (Section 2.2.2); added example in Section 7