Structure constants for the D-series Virasoro minimal models

TL;DR

This paper derives explicit expressions for the structure constants in D-series Virasoro minimal models, extending previous work on A-series models, and confirms their consistency through numerical tests.

Contribution

It provides the first detailed solution for boundary and bulk structure constants in D-series Virasoro minimal models, including their symmetry properties.

Findings

Structure constants are unique up to field redefinitions.

The structure constants exhibit a Z_2-symmetry.

Numerical tests confirm the consistency of the solutions.

Abstract

In this paper expressions are given for the bulk and boundary structure constants of D-series Virasoro minimal models on the upper half plane. It is the continuation of an earlier work on the A-series. The solution for the boundary theory is found first and then extended to the bulk. The modular invariant bulk field content is recovered as the maximal set of bulk fields consistent with the boundary theory. It is found that the structure constants are unique up to redefinition of the fields and in the chosen normalisation exhibit a manifest Z_2-symmetry associated to the D-diagram. The solution has been subjected to random numerical tests against the constraints it has to fulfill.