Liouville conformal blocks and Stokes phenomena

TL;DR

This paper derives braid group representations and Stokes matrices for Liouville conformal blocks with irregular operators, linking conformal field theory, Landau-Ginzburg models, and topological phases of matter.

Contribution

It introduces new braid group and Stokes matrix structures for Liouville conformal blocks with irregular operators, connecting CFT with topological quantum field theories.

Findings

Derived braid group representations for irregular conformal blocks

Connected conformal blocks to Landau-Ginzburg wavefunctions

Linked conformal blocks to topological phases via TQFT

Abstract

In this work we derive braid group representations and Stokes matrices for Liouville conformal blocks with one irregular operator. By employing the Coulomb gas formalism, the corresponding conformal blocks can be interpreted as wavefunctions of a Landau-Ginzburg model specified by a superpotential $\mathcal{W}$. Alternatively, these can also be viewed as wavefunctions of a 3d TQFT on a 3-ball with boundary a 2-sphere on which the operator insertions represent Anyons whose fusion rules describe novel topological phases of matter.