Local logarithmic correlators as limits of Coulomb gas integrals

Raoul Santachiara (1) , Jacopo Viti (2)

1 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
2 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]

We will describe how logarithmic singularities arise as limits of Coulomb Gas integrals. Our approach will combine analytic properties of the time-like Liouville structure constants, together with the recursive formula of the Virasoro conformal blocks. Although the Coulomb Gas formalism forces a diagonal coupling between the chiral and antichiral sectors of the Conformal Field Theory (CFT), we present new results for the multi-screening integrals which are potentially interesting for applications to critical statistical systems described by Logarithmic CFTs. In particular our findings extend and complement previous results, derived with Coulomb Gas methods, at $c=0$ and $c=-2$.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique des Hautes Energies - Théorie [hep-th]

Raoul Santachiara, Jacopo Viti. Local logarithmic correlators as limits of Coulomb gas integrals. Nuclear Physics B, 2014, 882, pp.229-262. ⟨10.1016/j.nuclphysb.2014.02.022⟩. ⟨hal-01006572⟩