Non-Perturbative Topological Strings And Conformal Blocks

TL;DR

This paper develops a non-perturbative framework for certain topological string theories using dual open string building blocks, establishing a connection with Liouville conformal blocks via matrix models with logarithmic potentials.

Contribution

It introduces a non-perturbative completion of topological strings through open string blocks and maps these to Liouville conformal blocks using matrix model contours and monodromy.

Findings

Established a correspondence between topological string blocks and Liouville conformal blocks.

Identified the role of matrix model contours in defining non-perturbative topological string theories.

Connected string interaction points to critical points of matrix potentials in light-cone diagrams.

Abstract

We give a non-perturbative completion of a class of closed topological string theories in terms of building blocks of dual open strings. In the specific case where the open string is given by a matrix model these blocks correspond to a choice of integration contour. We then apply this definition to the AGT setup where the dual matrix model has logarithmic potential and is conjecturally equivalent to Liouville conformal field theory. By studying the natural contours of these matrix integrals and their monodromy properties, we propose a precise map between topological string blocks and Liouville conformal blocks. Remarkably, this description makes use of the light-cone diagrams of closed string field theory, where the critical points of the matrix potential correspond to string interaction points.