Relating the Archetypes of Logarithmic Conformal Field Theory

Understand

Logarithmic conformal field theory is a rich and vibrant area of modern mathematical physics with well-known applications to both condensed matter theory and string theory.

• Our limited understanding of these theories is based upon detailed studies of various examples that one may regard as archetypal.
• These include the c=-2 triplet model, the Wess-Zumino-Witten model on SL(2;R) at level k=-1/2, and its supergroup analogue on GL(1|1).
• Here, the latter model is studied algebraically through representation theory, fusion and modular invariance, facilitating a subsequent investigation of its cosets and extended algebras.