W-Extended Logarithmic Minimal Models

Understand

We consider the continuum scaling limit of the infinite series of Yang-Baxter integrable logarithmic minimal models LM(p,p') as `rational' logarithmic conformal field theories with extended W symmetry.

• The representation content is found to consist of 6pp'-2p-2p' W-indecomposable representations of which 2p+2p'-2 are of rank 1, 4pp'-2p-2p' are of rank 2, while the remaining 2(p-1)(p'-1) are of rank 3.
• We identify these representations with suitable limits of Yang-Baxter integrable boundary conditions on the lattice.
• The W-indecomposable rank-1 representations are all W-irreducible while we present a conjecture for the embedding patterns of the W-indecomposable rank-2 and -3 representations.