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

J. Balog·P. Forgacs·L. Palla
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Abstract

An $S$-matrix is proposed for the two dimensional O(3) $σ$-model with a dynamical $θ$-term (axion model). Exploiting an Abelian T-duality transformation connecting the axion model to an integrable SU(2)$\times$U(1) symmetric principal $σ$-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) $σ$-model with a {\sl constant} $θ$-term, in contradistinction to the axion model, is illustrated by calculating the $2\to3$ particle production amplitude to lowest order in $θ$.

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J. Balog, P. Forgacs, L. Palla. 2000-04-26. A two-dimensional integrable axionic sigma-model and T-duality. https://doi.org/10.1016/s0370-2693(00)00645-6

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