Logarithmic Superconformal Minimal Models

Understand

The higher fusion level logarithmic minimal models LM(P,P';n) have recently been constructed as the diagonal GKO cosets (A_1^{(1)})_k oplus (A_1^{(1)})_n / (A_1^{(1)})_{k+n} where n>0 is an integer fusion level and k=nP/(P'-P)-2 is a fractional level.

• For n=1, these are the logarithmic minimal models LM(P,P').
• For n>1, we argue that these critical theories are realized on the lattice by n x n fusion of the n=1 models.
• For n=2, we call them logarithmic superconformal minimal models LSM(p,p') where P=|2p-p'|, P'=p' and p,p' are coprime, and they share the central charges of the rational superconformal minimal models SM(P,P').