Local logarithmic correlators as limits of Coulomb gas integrals

Abstract

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 $c=-2$.

38 pages, 12 figures

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• On 2d CFTs that interpolate between minimal models
• Two-point connectivity of two-dimensional critical $Q-$ Potts random clusters on the torus
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• On the CFT describing the spin clusters in 2d Potts model
• Level Set Percolation in Two-Dimensional Gaussian Free Field
• Uniform Spanning Tree in Topological Polygons, Partition Functions for SLE(8), and Correlations in $c=-2$ Logarithmic CFT
• Logarithmic operators in $c=0$ bulk CFTs
• The free field representation for the $GL(1|1)$ WZW model revisited
• Conformal amplitude hierarchy and the Poincare disk
• Crossing-symmetric Twist Field Correlators and Entanglement Negativity in Minimal CFTs