The algebraic curve of classical superstrings on \(\mathrm{AdS}_{5} \times S^{5}\)
type: Item
instance of: scholarly article
title: The algebraic curve of classical superstrings on \(\mathrm{AdS}_{5} \times S^{5}\)
zbMATH Open document ID: 1125.81037
author: Kazuhiro Sakai
author: Niklas Beisert
author: Vladimir A. Kazakov
author: K. Zarembo
published in: Communications in Mathematical Physics
publication date: 2006-11-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/hep-th/0502226
review text: From the authors' abstract: We investigate the monodromy of the Lax connection for classical IIB superstrings on \(\text{AdS}_5\times S^5\). For any solution of the equations of motions we derive a spectral curve of degree \(4+4\). The curve consists purely of conserved quantities, all gauge degrees of freedom have been eliminated in this form. The most relevant quantities of the solution, such as its energy, can be expressed through certain holomorphic integrals on the curve. This allows for a classification of finite gap solutions analogous to the general solution of strings in flat space. The role of fermions in the context of the algebraic curve is clarified. Finally, we derive a set of integral equations which reformulates the algebraic curve as a Riemann-Hilbert problem. They agree with the planar one-loop \(N=4\) supersymmetric gauge theory proving the complete agreement of spectra in this approximation.
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: 5076283
zbMATH Keywords: Lax pairs
zbMATH Keywords: sigma models
zbMATH Keywords: integrable models
zbMATH Keywords: string theory
MaRDI profile type: Publication
OpenAlex ID: W1980102218
Wikidata QID: Q59256204
arXiv ID: hep-th/0502226
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DOI: 10.1007/S00220-006-1529-4
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description: scientific article