Fusion rules and boundary conditions in the c=0 triplet model

TL;DR

This paper analyzes the fusion rules and boundary conditions of the c=0 logarithmic triplet model W_2,3, revealing a finite set of representations that close under fusion and identifying which yield consistent boundary conditions.

Contribution

It determines the fusion rules of irreducible representations from first principles and explores the boundary conditions specific to the W_2,3 model at c=0.

Findings

Fusion rules form a finite closed set of representations.

Only a subset of representations lead to consistent boundary conditions.

Boundary spectra exhibit non-degenerate two-point correlators.

Abstract

The logarithmic triplet model W_2,3 at c=0 is studied. In particular, we determine the fusion rules of the irreducible representations from first principles, and show that there exists a finite set of representations, including all irreducible representations, that closes under fusion. With the help of these results we then investigate the possible boundary conditions of the W_2,3 theory. Unlike the familiar Cardy case where there is a consistent boundary condition for every representation of the chiral algebra, we find that for W_2,3 only a subset of representations gives rise to consistent boundary conditions. These then have boundary spectra with non-degenerate two-point correlators.