Notes on the solutions of Zamolodchikov-type recursion relations in Virasoro minimal models

TL;DR

This paper investigates the solutions of Zamolodchikov-type recursion relations for Virasoro minimal models, focusing on singularities caused by resonances and their cancellation in conformal blocks and characters.

Contribution

It provides a detailed analysis of the singularities in recursion relations for Virasoro minimal models and demonstrates how these singularities cancel in the final conformal blocks and characters.

Findings

Resonance singularities occur during intermediate steps

Singularities cancel out in the final solutions

Enhanced understanding of recursion relations in minimal models

Abstract

We study Virasoro minimal-model 4-point conformal blocks on the sphere and 0-point conformal blocks on the torus (the Virasoro characters), as solutions of Zamolodchikov-type recursion relations. In particular, we study the singularities due to resonances of the dimensions of conformal fields in minimal-model representations, that appear in the intermediate steps of solving the recursion relations, but cancel in the final results.