(0,2) Elephants

TL;DR

This paper compares methods for counting massless E6 singlets in heterotic string compactifications on Calabi-Yau threefolds across different geometric and algebraic limits, revealing how spectra change with moduli deformations.

Contribution

It introduces a comprehensive comparison of singlet counts in various phases of heterotic compactifications and clarifies the relationships and state vanishings during moduli deformations.

Findings

Singlet counts differ across large radius, Landau-Ginzburg, and orbifold limits.

States can be matched and identified between phases.

Extra singlets appear at specific complex structure values, independent of Kähler moduli.

Abstract

We enumerate massless E6 singlets for (0,2)-compactifications of the heterotic string on a Calabi-Yau threefold with the "standard embedding" in three distinct ways. In the large radius limit of the threefold, these singlets count deformations of the Calabi-Yau together with its tangent bundle. In the "small-radius" limit we apply Landau-Ginzburg methods. In the orbifold limit we use a combination of geometry and free field methods. In general these counts differ. We show how to identify states between these phases and how certain states vanish from the massless spectrum as one deforms the complex structure or Kaehler form away from the Gepner point. The appearance of extra singlets for particular values of complex structure is explored in all three pictures, and our results suggest that this does not depend on the Kaehler moduli.