The supersymmetry index and the construction of modular invariants
Let G be a rank \(\ell\) semisimple Lie group whose Lie algebra is used to construct a Kac-Moody algebra [\textit{V. G. Kac}, Infinite dimensional Lie algebras (1985; Zbl 0574.17010)]. An identity derived in a previous paper for any supersymmetric coset model [\textit{W. Lerche}, \textit{C. Vafa}, and the author, Nucl. Phys. B 324, 427-474 (1989)] is applied here in order to study the modular properties of affine G-characters via the modular properties of the affine characters of rank \(\ell\) semisimple subgroups of G (except possibly for U(1) factors). Applications of this relationship are then given; in particular, an algorithm for generating modular invariant combinations of affine G-characters and a way to classify modular invariants of affine G-representations.
scientific article; zbMATH DE number 4171184