Liouville theory with a central charge less than one

Sylvain Ribault 1, * Raoul Santachiara 2

Journal of High Energy Physics, Springer Verlag (Germany), 2015, pp.109. <10.1007/JHEP08(2015)109>

We determine the spectrum and correlation functions of Liouville theory with a central charge less than (or equal) one. This completes the definition of Liouville theory for all complex values of the central charge. The spectrum is always spacelike, and there is no consistent timelike Liouville theory. We also study the non-analytic conformal field theories that exist at rational values of the central charge. Our claims are supported by numerical checks of crossing symmetry. We provide Python code for computing Virasoro conformal blocks, and correlation functions in Liouville theory and (generalized) minimal models.

  • 1. IPHT - Institut de Physique Théorique - UMR CNRS 3681
  • 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques