Integrable QFT(2) Encoded on Products of Dynkin Diagrams
Abstract
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)]
- Publication:
-
arXiv e-prints
- Pub Date:
- November 1993
- DOI:
- 10.48550/arXiv.hep-th/9311116
- arXiv:
- arXiv:hep-th/9311116
- Bibcode:
- 1993hep.th...11116Q
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- 17p (latex), Bologna preprint DFUB-93-11