A two-dimensional integrable axionic sigma-model and T-duality

Abstract

An $S$-matrix is proposed for the two dimensional O(3) $\sigma$-model with a dynamical $\theta$-term (axion model). Exploiting an Abelian T-duality transformation connecting the axion model to an integrable SU(2)$\times$U(1) symmetric principal $\sigma$-model, strong evidence is presented for the correctness of the proposed $S$-matrix by comparing the perturbatively calculated free energies with the ones based on the Thermodynamical Bethe Ansatz. This T-duality transformation also leads to a new Lax-pair for both models. The quantum non-integrability of the O(3) $\sigma$-model with a {\sl constant} $\theta$-term, in contradistinction to the axion model, is illustrated by calculating the $2\to 3$ particle production amplitude to lowest order in $\theta$.

11 pages, LaTeX

References in corpus (3)

• Duality Beyond the First Loop
• Poisson-Lie T-Duality beyond the classical level and the renormalization group
• Thermodynamical Bethe Ansatz analysis in an SU(2)xU(1) symmetric sigma-model

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