Modular Invariant Partition Functions and Method of Shift Vector

H. Arfaei; A. Shirzad

doi:10.1063/1.530770

paper

Modular Invariant Partition Functions and Method of Shift Vector

arXiv:hep-th/9301016 · doi:10.1063/1.530770

Abstract

Using shift vector method we obtain a large class of self-dual lattices of dimension $(l, l)$ , which has a one to one correspondence with modular invariants of free bosonic theory compactified on co-root lattice of a rank $l$ Lie group. Then a large number of modular invariants of affine Lie algebras are derived explicitly. As two applications of this method, we give a direct derivation of $D$ -series of $S U (N)$ and a new proof for the A-D-E classification of the $S U (2)_{k}$ partition functions.

28 pages, Plaintex file, BONN-HE-93-1, SUTDP/93/71/1