The Quantum Spectrum of the Conserved Charges in Affine Toda Theories

TL;DR

This paper computes the exact eigenvalues of conserved charges in affine Toda theories using a free field realization, confirming their RG invariance and classical limits, and connecting to known quantum mass results.

Contribution

It introduces a novel free field realization of the Zamolodchikov-Faddeev algebra to determine conserved charge eigenvalues in affine Toda theories.

Findings

Eigenvalues are RG invariant and match classical limits.

Recovers known quantum mass formulas for n=1.

Eigenvalues pass perturbation theory checks.

Abstract

The exact eigenvalues of the infinite set of conserved charges on the multi-particle states in affine Toda theories are determined. This is done by constructing a free field realization of the Zamolodchikov-Faddeev algebra in which the conserved charges are realized as derivative operators. The resulting eigenvalues are renormalization group (RG) invariant, have the correct classical limit and pass checks in first order perturbation theory. For $n=1$ one recovers the (RG invariant form of the) quantum masses of Destri and DeVega.