Integrable deformations of CFTs and the discrete Hirota equations

Abstract

We solve the discrete Hirota equations (Kirillov-Reshetikhin Q-systems) for $A_r$, and their analogue for $D_r$, for the cases where the second variable ranges over either a finite set or over all integers. Until now only special solutions were known. We find all solutions for which no component vanishes, as required in the known applications. As an introduction we present the known solution where the second variable ranges over the natural numbers.

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References in corpus (1)

• Proof of the combinatorial Kirillov-Reshetikhin conjecture

Cited by in corpus (4)

• Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras I: Type B_r
• Positivity and periodicity of $Q$-systems in the WZW fusion ring
• Linear recurrence relations in $Q$-systems and difference $L$-operators
• CFTs on Riemann Surfaces of genus $g\ge 1$: Dependence on moduli