Algebraic curve for the SO(6) sector of AdS/CFT
type: Item
instance of: scholarly article
title: Algebraic curve for the SO(6) sector of AdS/CFT
zbMATH Open document ID: 1125.81036
author: Kazuhiro Sakai
author: Niklas Beisert
author: Vladimir A. Kazakov
published in: Communications in Mathematical Physics
publication date: 2006-11-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/hep-th/0410253
review text: 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.
reviewed by: M. Schlichenmaier
Mathematics Subject Classification ID: 81T30
Mathematics Subject Classification ID: 83E30
Mathematics Subject Classification ID: 81R12
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 14H70
zbMATH DE Number: 5076282
zbMATH Keywords: Lax pairs, sigma models
zbMATH Keywords: integrable models
zbMATH Keywords: string theory
MaRDI profile type: Publication
OpenAlex ID: W2083877406
Wikidata QID: Q59256198
arXiv ID: hep-th/0410253
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DOI: 10.1007/S00220-005-1528-X
description: scientific article