Connectivities of Potts Fortuin-Kasteleyn clusters and time-like Liouville correlator

Marco Picco 1, Raoul Santachiara 2, Jacopo Viti 3, Gesualdo Delfino 4

Nuclear Physics B 875, 3 (2013) 719

Recently, two of us argued that the probability that an FK cluster in the Q-state Potts model connects three given points is related to the time-like Liouville three-point correlation function. Moreover, they predicted that the FK three-point connectivity has a prefactor which unveils the effects of a discrete symmetry, reminiscent of the S_Q permutation symmetry of the Q=2,3,4 Potts model. Their theoretical prediction has been checked numerically for the case of percolation, corresponding to Q=1. We introduce the time-like Liouville correlator as the only consistent analytic continuation of the minimal model structure constants and present strong numerical tests of the relation between the time-like Liouville correlator and percolative properties of the FK clusters for real values of Q.

  • 1 : Laboratoire de Physique Théorique et Hautes Energies (LPTHE)
    CNRS : UMR7589 – Université Pierre et Marie Curie (UPMC) - Paris VI – Université Paris VII - Paris Diderot
  • 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 3 : Laboratoire de Physique Théorique de l'ENS (LPTENS)
    CNRS : UMR8549 – Université Pierre et Marie Curie (UPMC) - Paris VI – École normale supérieure [ENS] - Paris
  • 4 : Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies (SISSA / ISAS)
    Scuola Internazionale Superiore di Studi Avanzati/International School for Advanced Studies (SISSA/ISAS)