Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-11-11
JHEP 0307 (2003) 031
Physics
High Energy Physics
High Energy Physics - Theory
Journal version: references added and minor corrections performed
Scientific paper
10.1088/1126-6708/2003/07/031
The nonlinear integral equations describing the spectra of the left and right (continuous) quantum KdV equations on the cylinder are derived from integrable lattice field theories, which turn out to allow the Bethe Ansatz equations of a twisted ``spin -1/2'' chain. A very useful mapping to the more common nonlinear integral equation of the twisted continuous spin $+1/2$ chain is found. The diagonalization of the transfer matrix is performed. The vacua sector is analysed in detail detecting the primary states of the minimal conformal models and giving integral expressions for the eigenvalues of the transfer matrix. Contact with the seminal papers \cite{BLZ, BLZ2} by Bazhanov, Lukyanov and Zamolodchikov is realised. General expressions for the eigenvalues of the infinite-dimensional abelian algebra of local integrals of motion are given and explicitly calculated at the free fermion point.
Fioravanti Davide
Rossi Marco
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