# Logarithmic Minimal Models, Critical Dense Polymers, Symplectic Fermions and Fusion Rules

#### by Paul Pearce

Institution: The University of Melbourne
Date: Mon 5th May 2008
Time: 1:00 PM
Location: Room 213 Richard Berry Building, The University of Melbourne

Abstract: The logarithmic minimal models LM(p,pâ€™) with p, pâ€™ coprime are a family of
Yang-Baxter integrable two-dimensional lattice models. The first members of this family
are critical dense polymers LM(1,2) and critical percolation LM(2,3). Remarkably, critical
dense polymers is exactly solvable on a finite lattice. The continuum scaling limit of
these theories yield logarithmic conformal field theories characterized by the existence
of reducible yet indecomposable representations of the Virasoro algebra or extended
conformal algebra. In the extended W-algebra picture, LM(1,2) is identified with symplectic
fermions. The fusion rules for LM(1,2) are presented in both the Virasoro and extended
W-algebra pictures and their relationship explained.