Nondiagonal $CP_m$ Coset Models and their Poincar\'E Polynomials

TL;DR

This paper constructs Poincaré polynomials for nondiagonal $CP_m$ coset models, enabling the calculation of chiral generations in string compactifications and exploring discrete symmetry modding.

Contribution

It introduces Poincaré polynomials for nondiagonal $CP_m$ coset models, advancing the understanding of their chiral rings and implications for string theory.

Findings

Poincaré polynomials for these coset models are explicitly constructed.

The number of chiral generations in string compactifications is computed.

Discussions on modding by discrete symmetries are included.

Abstract

$N=2$ coset models of the type $SU(m+1)/SU(m)\times U(1)$ with nondiagonal modular invariants for both $SU(m+1)$ and $SU(m)$ are considered. Poincar\'e polynomials of the corresponding chiral rings of these algebras are constructed. They are used to compute the number of chiral generations of the associated string compactifications. Moddings by discrete symmetries are also discussed.