Abstract
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.
Citation
A. Bytsko. J. Teschner. "The integrable structure of nonrational conformal field theory." Adv. Theor. Math. Phys. 17 (4) 701 - 740, August 2013.