Counting charged massless states in the (0,2) heterotic CFT/geometry connection

TL;DR

This paper develops methods to compute charged massless states in heterotic (0,2) CFTs using simple current techniques, relating algebraic formulas to geometric data, and explores implications for string model building.

Contribution

It introduces explicit formulas for charged spectra in heterotic models via Poincaré polynomials and elliptic genera, extending analysis to non-rational cases and various gauge groups.

Findings

Explicit spectrum formulas for heterotic SO(10) models

Inclusion of non-BPS state contributions

Applicability to Landau-Ginzburg orbifold models

Abstract

We use simple current techniques and their relation to orbifolds with discrete torsion for studying the (0,2) CFT/geometry duality with non-rational internal N=2 SCFTs. Explicit formulas for the charged spectra of heterotic SO(10) GUT models are computed in terms of their extended Poincar\'{e} polynomials and the complementary Poincar\'{e} polynomial which can be computed in terms of the elliptic genera. While non-BPS states contribute to the charged spectrum, their contributions can be determined also for non-rational cases. For model building, with generalizations to SU(5) and SM gauge groups, one can take advantage of the large class of Landau-Ginzburg orbifold examples.