The integrable structure of nonrational conformal field theory. (English) Zbl 1431.81135

Summary: Using the example of Liouville theory, we show how the separation into left- and right-moving degrees of freedom in a nonrational conformal field theory can be made explicit in terms of its integrable structure. The key observation is that there exist separate Baxter Q-operators for left and right-moving degrees of freedom. Combining a study of the analytic properties of the Q-operators with Sklyanin’s Separation of Variables Method leads to a complete characterization of the spectrum. Taking the continuum limit allows us in particular to rederive the Liouville reflection amplitude using only the integrable structure.


81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81R12 Groups and algebras in quantum theory and relations with integrable systems
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