Algebraic curve for the SO(6) sector of AdS/CFT
The article deals with integrability in the context of models of string theory on \(\text{AdS}_5\times S^5\). As usual also in this case integrability is closely related to Lax pairs and associated curves. From the introduction: ``\dots we make a new step in direction of construction of the full algebraic curve of the classical \(\text{AdS}_5\times S^5\) sigma model and of its perturbative counterpart on the SYM side following from the one-loop integrability of the full SYM theory \dots We accomplish this program for the so(6) sector of SYM, which is closed at one-loop as well as in the thermodynamic limit\dots, and its dual, the sigma model for the string on \(\mathbb R_t\times S^5\). We show in both theories that the projection of the algebraic curve onto the complex plane is a Riemann surface with four sheets corresponding to the four-dimensional chiral spinor representation of \(\text{SU}(4)\sim \text{SO}(6)\). In the SYM case such a curve solves the classical limit of the corresponding Bethe equations. We will identify and fix all the parameters of this curve on both sides of AdS/CFT.'' One of the main tools used are transfer matrices in the algebraic Bethe ansatz framework.
scientific article