Logarithmic superconformal minimal models

Abstract

The higher fusion level logarithmic minimal models LM(P; P'; n) have recently been constructed as the diagonal GKO cosets (A(1) 1)k (A(1)1)n/(A (1)1)k+n where n ≥ 1 is an integer fusion level and k = nP/(P' - P) - 2 is a fractional level. For n = 1, these are the well-studied logarithmic minimal models LM(P, P') ≡ LM(P; P'; 1). For n = 2, we argue that these critical theories are realized on the lattice by n × n fusion of the n = 1 models. We study the critical fused lattice models LM(p, p')n×n within a lattice approach and focus our study on the n = 2 models. We call these logarithmic superconformal minimal models LSM(p, p') ≡ LM(P, P'; 2) where P = |2p - p'|, P' = p' and p' p' are coprime...