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 × ADE and a simple formula for the ultraviolet perturbing operator conformal dimensions only in terms of rank and Coxeter numbers of ADE × ADE. We conclude with some remarks on the curious case ADE × D.
Integrable QFT in two-dimensions encoded on products of Dynkin diagrams
TATEO, Roberto
1995-01-01
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 × ADE and a simple formula for the ultraviolet perturbing operator conformal dimensions only in terms of rank and Coxeter numbers of ADE × ADE. We conclude with some remarks on the curious case ADE × D.
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