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An elliptic parameterisation of the Zamolodchikov model

Bazhanov, Vladimir; Mangazeev, Vladimir; Okada, Yuichiro; Sergeev, Sergey M.

Description

The Zamolodchikov model describes an exact relativistic factorized scattering theory of straight strings in (2. +. 1)-dimensional space-time. It also defines an integrable 3D lattice model of statistical mechanics and quantum field theory. The three-string S-matrix satisfies the tetrahedron equation which is a 3D analog of the Yang-Baxter equation. Each S-matrix depends on three dihedral angles formed by three intersecting planes, whereas the tetrahedron equation contains five independent...[Show more]

dc.contributor.authorBazhanov, Vladimir
dc.contributor.authorMangazeev, Vladimir
dc.contributor.authorOkada, Yuichiro
dc.contributor.authorSergeev, Sergey M.
dc.date.accessioned2015-12-13T22:22:41Z
dc.identifier.issn0550-3213
dc.identifier.urihttp://hdl.handle.net/1885/72363
dc.description.abstractThe Zamolodchikov model describes an exact relativistic factorized scattering theory of straight strings in (2. +. 1)-dimensional space-time. It also defines an integrable 3D lattice model of statistical mechanics and quantum field theory. The three-string S-matrix satisfies the tetrahedron equation which is a 3D analog of the Yang-Baxter equation. Each S-matrix depends on three dihedral angles formed by three intersecting planes, whereas the tetrahedron equation contains five independent spectral parameters, associated with angles of an Euclidean tetrahedron. The vertex weights are given by rather complicated expressions involving square roots of trigonometric function of the spectral parameters, which is quite unusual from the point of view of 2D solvable lattice models. In this paper we consider a particular four-parameter specialisation of the tetrahedron equation when one of its vertices goes to infinity and the tetrahedron itself degenerates into an infinite prism. We show that in this limit all the vertex weights in the tetrahedron equation can be represented as meromorphic functions on an elliptic curve. Moreover we show that a special reduction of the tetrahedron equation in this case leads precisely to an example of the tetrahedral Zamolodchikov algebra, previously constructed by Korepanov. This algebra plays important role for a "layered" construction of the Shastry's R-matrix and the 2D S-matrix appearing in the problem of the ADS/CFT correspondence for N=4 SUSY Yang-Mills theory in four dimensions. Possible applications of our results in this field are briefly discussed.
dc.publisherElsevier
dc.rightsAuthor/s retain copyright
dc.sourceNuclear Physics B
dc.titleAn elliptic parameterisation of the Zamolodchikov model
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume871
dc.date.issued2013
local.identifier.absfor010500 - MATHEMATICAL PHYSICS
local.identifier.ariespublicationf5625xPUB3210
local.type.statusPublished Version
local.contributor.affiliationBazhanov, Vladimir, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationMangazeev, Vladimir, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationOkada, Yuichiro, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationSergeev, Sergey M., University of Canberra
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage127
local.bibliographicCitation.lastpage144
local.identifier.doi10.1016/j.nuclphysb.2013.02.011
dc.date.updated2015-12-11T07:58:07Z
local.identifier.scopusID2-s2.0-84875381705
local.identifier.thomsonID000316712300007
dcterms.accessRightsOpen Access
CollectionsANU Research Publications

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