Boundary structure constants for the A-series Virasoro minimal models

TL;DR

This paper derives a specific form of boundary and bulk structure constants for A-series Virasoro minimal models on the upper half plane, expressed via F-matrix elements, aiding in conformal field theory calculations.

Contribution

It provides explicit formulas for structure constants in Virasoro minimal models based on sewing constraints and F-matrices, facilitating numerical and analytical work.

Findings

Structure constants expressed in terms of F-matrix elements

Recursion relation for F-matrices provided

Numerical tests show consistency with known results

Abstract

We consider A-series modular invariant Virasoro minimal models on the upper half plane. From Lewellen's sewing constraints a necessary form of the bulk and boundary structure constants is derived. Necessary means that any solution can be brought to the given form by rescaling of the fields. All constants are expressed essentially in terms of fusing (F-) matrix elements and the normalisations are chosen such that they are real and no square roots appear. It is not shown in this paper that the given structure constants solve the sewing constraints, however random numerical tests show no contradiction and agreement of the bulk structure constants with Dotsenko and Fateev. In order to facilitate numerical calculations a recursion relation for the F-matrices is given.