A Proof of the KNS conjecture : $D_r$ case

TL;DR

This paper proves the KNS conjecture for type D_r by deriving an explicit formula for the quantum dimension solution of the Q-system, which is significant for dilogarithm identities in conformal field theory.

Contribution

It provides the first proof of the KNS conjecture for type D_r and introduces explicit formulas for the quantum dimension solutions of the Q-system.

Findings

Proof of the KNS conjecture for type D_r.

Explicit formula for the positive solution of the Q-system.

Application to dilogarithm identities in conformal field theories.

Abstract

We prove the Kuniba-Nakanishi-Suzuki (KNS) conjecture concerning the quantum dimension solution of the $Q$-system of type $D_r$ obtained by a certain specialization of classical characters of the Kirillov-Reshetikhin modules. To this end, we use various symmetries of quantum dimensions. As a result, we obtain an explicit formula for the positive solution of the level $k$ restricted $Q$-system of type $D_r$ which plays an important role in dilogarithm identities for conformal field theories.