Mapping moduli across heterotic conifolds

TL;DR

This paper provides strong evidence for a duality between heterotic string compactifications on Calabi-Yau manifolds connected by conifold transitions, demonstrating the matching of effective theories and a large number of holomorphic functions.

Contribution

It constructs a duality map for heterotic conifold transitions and verifies the agreement of superpotential couplings, strengthening the evidence for heterotic dualities.

Findings

147,440 superpotential Yukawa couplings match across the duality

Duality map aligns holomorphic functions in effective theories

Special cases reduce to target space duality of (0,2) GLSMs

Abstract

In this work, we provide evidence for a duality between 4-dimensional Calabi-Yau compactifications of the heterotic string, in which the base manifolds are linked by a conifold transition. In recent work, a geometric proposal was put forward for how 5-branes and gauge bundles are carried across such transitions. It was observed that compactifications connected in this way lead to 4-dimensional effective theories with the same massless spectrum. Here we provide much stronger evidence that these heterotic conifold transitions do indeed lead to dual theories. We construct a duality map between the field spaces of the two compactifications and use it to demonstrate the agreement of large numbers of holomorphic functions appearing in the definition of the effective theories. In an example, we show that 147,440 independent superpotential Yukawa couplings agree across the duality as holomorphic functions of the moduli. In certain special cases, the putative duality studied here reduces to the target space duality of (0,2) gauged linear sigma models.