Integrable QFT(2) Encoded on Products of Dynkin Diagrams

Details Integrable QFT(2) Encoded on Products of Dynkin Diagrams Integrable QFT(2) Encoded on Products of Dynkin Diagrams

1993-11-19

arxiv.org/abs/hep-th/9311116v1

Physics

High Energy Physics

High Energy Physics - Theory

17p (latex), Bologna preprint DFUB-93-11

Scientific paper

A large class of Thermodynamic Bethe Ansatz equations governing the Renormalization Group evolution of the Casimir energy of the vacuum on the cylinder for an integrable two-dimensional field theory, can often be encoded on a tensor product of two graphs. We demonstrate here that in this case the two graphs can only be of $ADE$ type. We also give strong numerical evidence for a new large set of Dilogarithm sum Rules connected to $ADE\times ADE$ and a simple formula for the ultraviolet perturbing operator conformal dimensions only in terms of rank and Coxeter numbers of $ADE\times ADE$. We conclude with some remarks on the curious case $ADE\times D$. [Talk given by F.R. at the Cargese Workshop "New Developments in String Theory, Conformal Models and Topological Field Theory" (May 1993)]

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