An elliptic parameterisation of the Zamolodchikov model

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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 spacetime. It also defines an integrable 3D lattice model of statistical mechanics and quantum field theory. The threestring Smatrix satisfies the tetrahedron equation which is a 3D analog of the YangBaxter equation. Each Smatrix depends on three dihedral angles formed by three intersecting planes, whereas the tetrahedron equation contains five independent...[Show more]
dc.contributor.author  Bazhanov, Vladimir  

dc.contributor.author  Mangazeev, Vladimir  
dc.contributor.author  Okada, Yuichiro  
dc.contributor.author  Sergeev, Sergey M.  
dc.date.accessioned  20151213T22:22:41Z  
dc.identifier.issn  05503213  
dc.identifier.uri  http://hdl.handle.net/1885/72363  
dc.description.abstract  The Zamolodchikov model describes an exact relativistic factorized scattering theory of straight strings in (2. +. 1)dimensional spacetime. It also defines an integrable 3D lattice model of statistical mechanics and quantum field theory. The threestring Smatrix satisfies the tetrahedron equation which is a 3D analog of the YangBaxter equation. Each Smatrix 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 fourparameter 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 Rmatrix and the 2D Smatrix appearing in the problem of the ADS/CFT correspondence for N=4 SUSY YangMills theory in four dimensions. Possible applications of our results in this field are briefly discussed.  
dc.publisher  Elsevier  
dc.rights  Author/s retain copyright  
dc.source  Nuclear Physics B  
dc.title  An elliptic parameterisation of the Zamolodchikov model  
dc.type  Journal article  
local.description.notes  Imported from ARIES  
local.identifier.citationvolume  871  
dc.date.issued  2013  
local.identifier.absfor  010500  MATHEMATICAL PHYSICS  
local.identifier.ariespublication  f5625xPUB3210  
local.type.status  Published Version  
local.contributor.affiliation  Bazhanov, Vladimir, College of Physical and Mathematical Sciences, ANU  
local.contributor.affiliation  Mangazeev, Vladimir, College of Physical and Mathematical Sciences, ANU  
local.contributor.affiliation  Okada, Yuichiro, College of Physical and Mathematical Sciences, ANU  
local.contributor.affiliation  Sergeev, Sergey M., University of Canberra  
local.bibliographicCitation.issue  1  
local.bibliographicCitation.startpage  127  
local.bibliographicCitation.lastpage  144  
local.identifier.doi  10.1016/j.nuclphysb.2013.02.011  
dc.date.updated  20151211T07:58:07Z  
local.identifier.scopusID  2s2.084875381705  
local.identifier.thomsonID  000316712300007  
dcterms.accessRights  Open Access  
Collections  ANU Research Publications 
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