Contents Online

# Advances in Theoretical and Mathematical Physics

## Volume 17 (2013)

### Number 4

### The integrable structure of nonrational conformal field theory

Pages: 701 – 740

DOI: http://dx.doi.org/10.4310/ATMP.2013.v17.n4.a1

#### Authors

#### 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.