Thermodynamics of the Complex su(3) Toda Theory

TL;DR

This paper computes the thermodynamic properties of the complex su(3) Toda theory using a new string hypothesis, confirming some aspects of the scattering theory while revealing new complexities in the attractive regime.

Contribution

It introduces a novel string hypothesis for the complex su(3) Toda theory and extends the understanding of its thermodynamics and scattering properties.

Findings

Confirmed the completeness of the soliton scattering theory in the repulsive regime.

Showed unitarity does not follow from the monodromy matrix eigenvalues.

Discovered complex bound state structures in the attractive regime, involving E6 and E8.

Abstract

We present the first computation of the thermodynamic properties of the complex su(3) Toda theory. This is possible thanks to a new string hypothesis, which involves bound states that are non self-conjugate solutions of the Bethe equations. Our method provides equivalently the solution of the su(3) generalization of the XXZ chain. In the repulsive regime, we confirm that the scattering theory proposed over the past few years - made only of solitons with non diagonal S-matrices - is complete. But we show that unitarity does not follow, contrary to early claims, eigenvalues of the monodromy matrix not being pure phases. In the attractive regime, we find that the proposed minimal solution of the bootstrap equations is actually far from being complete. We discuss some simple values of the couplings, where, instead of the few conjectured breathers, a very complex structure (involving E_6, or two E_8) of bound states is necessary to close the bootstrap.