Non-unitarity in quantum affine Toda theory and perturbed conformal field theory. (English) Zbl 0943.81041
Summary: There has been some debate about the validity of quantum affine Toda field theory at imaginary coupling, owing to the non-unitarity of the action, and consequently of its usefulness as a model of perturbed conformal field theory. Drawing on our recent work, we investigate the two simplest affine Toda theories for which this is an issue – \(a_2^{(1)}\) and \(a_2^{(2)}\). By investigating the \(S\)-matrices of these theories before RSOS restriction, we show that quantum Toda theory (with or without RSOS restriction) indeed has some fundamental problems, but that these problems are of two different sorts. For \(a_2^{(1)}\), the scattering of solitons and breathers is flawed in both classical and quantum theories, and RSOS restriction cannot solve this problem. For \(a_2^{(2)}\) however, while there are no problems with breather-soliton scattering there are instead difficulties with soliton-excited soliton scattering in the unrestricted theory. After RSOS restriction, the problems with kink-excited kink may be cured or may remain, depending in part on the choice of gradation, as we found earlier. We comment on the importance of regradations, and also on the survival of \(R\)-matrix unitarity and the \(S\)-matrix bootstrap in these circumstances.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81R99 | Groups and algebras in quantum theory |
| 81U20 | \(S\)-matrix theory, etc. in quantum theory |
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