Dynkin TBA's

TL;DR

This paper proves an identity for ADE minimal S-matrices that simplifies the TBA transformation, revealing a universal structure and uncovering new RG flows, with implications for higher rank algebras and dualities.

Contribution

It establishes a universal identity for ADE TBA systems, showing they can be encoded on A, D, E, and A/Z_2 graphs, and explores new RG flows and dualities.

Findings

Unified encoding of ADE TBA systems on specific graphs

Discovery of new massive and massless RG flows

Connection with level-rank duality

Abstract

We prove a useful identity valid for all $ADE$ minimal S-matrices, that clarifies the transformation of the relative thermodynamic Bethe Ansatz (TBA) from its standard form into the universal one proposed by Al.B.Zamolodchikov. By considering the graph encoding of the system of functional equations for the exponentials of the pseudoenergies, we show that any such system having the same form as those for the $ADE$ TBA's, can be encoded on $A,D,E,A/Z_2$ only. This includes, besides the known $ADE$ diagonal scattering, the set of all $SU(2)$ related {\em magnonic} TBA's. We explore this class sistematically and find some interesting new massive and massless RG flows. The generalization to classes related to higher rank algebras is briefly presented and an intriguing relation with level-rank duality is signalled.