Indecomposability parameters in chiral Logarithmic Conformal Field Theory

Understand

Work of the last few years has shown that the key algebraic features of Logarithmic Conformal Field Theories (LCFTs) are already present in some finite lattice systems (such as the XXZ spin-1/2 chain) before the continuum limit is taken.

• This has provided a very convenient way to analyze the structure of indecomposable Virasoro modules and to obtain fusion rules for a variety of models such as (boundary) percolation etc.
• LCFTs allow for additional quantum numbers describing the fine structure of the indecomposable modules, and generalizing the `b-number' introduced initially by Gurarie for the c=0 case.
• The determination of these indecomposability parameters has given rise to a lot of algebraic work, but their physical meaning has remained somewhat elusive.