Modular Constraints on Calabi-Yau Compactifications

TL;DR

This paper establishes universal constraints on the spectrum of non-BPS states in 2D supersymmetric sigma-models with Calabi-Yau targets, linking geometric properties to conformal field theory spectra.

Contribution

It provides the first global bounds on non-BPS states in Calabi-Yau compactifications, relating Hodge numbers to conformal weights and state counts.

Findings

Non-BPS primary states with conformal weights less than 0.656 must exist for large Hodge numbers.

The number of such non-BPS states grows at least linearly with the Hodge number.

Results have implications for the geometry and physics of Calabi-Yau compactifications.

Abstract

We derive global constraints on the non-BPS sector of supersymmetric 2d sigma-models whose target space is a Calabi-Yau manifold. When the total Hodge number of the Calabi-Yau threefold is sufficiently large, we show that there must be non-BPS primary states whose total conformal weights are less than 0.656. Moreover, the number of such primary states grows at least linearly in the total Hodge number. We discuss implications of these results for Calabi-Yau geometry.