Exact conserved quantities on the cylinder I: conformal case | Zendy

Davide Fioravanti | Zendy; Marco Rossi | Zendy

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Exact conserved quantities on the cylinder I: conformal case

Author(s) -

Davide Fioravanti,

Marco Rossi

Publication year - 2003

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2003/07/031

Subject(s) - bethe ansatz , integrable system , transfer matrix , conformal map , eigenvalues and eigenvectors , mathematical physics , nonlinear system , korteweg–de vries equation , integral equation , physics , conformal field theory , conserved quantity , mathematics , mathematical analysis , quantum mechanics , computer science , computer vision

The nonlinear integral equations describing the spectra of the left and right(continuous) quantum KdV equations on the cylinder are derived from integrablelattice field theories, which turn out to allow the Bethe Ansatz equations of atwisted ``spin -1/2'' chain. A very useful mapping to the more common nonlinearintegral equation of the twisted continuous spin $+1/2$ chain is found. Thediagonalization of the transfer matrix is performed. The vacua sector isanalysed in detail detecting the primary states of the minimal conformal modelsand giving integral expressions for the eigenvalues of the transfer matrix.Contact with the seminal papers \cite{BLZ, BLZ2} by Bazhanov, Lukyanov andZamolodchikov is realised. General expressions for the eigenvalues of theinfinite-dimensional abelian algebra of local integrals of motion are given andexplicitly calculated at the free fermion point.Comment: Journal version: references added and minor corrections performe

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