Advances in Theoretical and Mathematical Physics

Volume 17 (2013)

Number 4

The integrable structure of nonrational conformal field theory

Pages: 701 – 740



A. Bytsko (Steklov Mathematics Institute, St. Petersburg, Russia)

J. Teschner (DESY Theory, Hamburg, Germany)


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.

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