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

TL;DR

This paper explores the algebraic structure of transfer matrices and Yang-Baxter equations on the string worldsheet in AdS(5) x S(5), revealing new insights into integrability via Wilson lines and r- and s-matrices.

Contribution

It introduces a formalism connecting transfer matrices and Yang-Baxter equations in the string theory context using the pure spinor approach.

Findings

Transfer matrices relate to Wilson lines with insertions.

r- and s-matrices satisfy a generalized classical Yang-Baxter equation.

Formalism simplifies for infinite or closed Wilson lines.

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.