Towards a Classification of su(2)(direct sum)...(direct sum)su(2) ModularInvariant Partition Functions

摘要

The complete classification of WZNW modular invariant partition functions isknown for very few affine algebras and levels, the most significant being all levels of A(sub 1) and A(sub 2) and level 1 of all simple algebras. Here, the authors address the classification problem for the nicest high rank semi-simple affine algebras: A(sub 1, sup (1))sup (+ circled)r. Among other things, they explicitly find all automorphism invariants, for all levels k=(k(sub 1),..., k(sub r)), and complete the classification for A(sub 1, sup (1)) (+ circled) A(sub 1, sup (1)), for all levels k(sub 1), k(sub 2). They also solve the classification problem for A(sub 1, sup (1))sup (+ circled)r, for any levels k(sub i). In addition, they find some physical invariants which seem to be new.