The integrable structure of nonrational conformal field theory

Details The integrable structure of nonrational conformal field theory The integrable structure of nonrational conformal field theory

2009-02-27

arxiv.org/abs/0902.4825v2

Physics

High Energy Physics

High Energy Physics - Theory

34 pages; typos corrected, comments added

Scientific paper

Using the example of Liouville theory, we show how the separation into left- and rightmoving degrees of freedom of 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.

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