Mapping moduli across heterotic conifolds

TL;DR

This paper investigates whether heterotic string compactifications connected by Calabi–Yau conifold transitions are truly dual theories. By constructing a field-space mapping anchored in bridging-brane geometry and constrained by the conifold middle, the authors compare gauge-kinetic functions and the full holomorphic Yukawa sector across dual pairs. They demonstrate strong evidence for duality by showing exact matching of large sets of Yukawa couplings (e.g., 147,440) and consistent moduli mappings in both brane and bundle settings. The results point toward a novel N=1 duality in four dimensions and motivate further study of nonperturbative effects and extensions to broader string-theory contexts.

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.

Figures (2)

• Figure 1: In a Calabi-Yau conifold transition, two smooth Calabi-Yau manifolds (denoted $X_D$ for deformation and $X_R$ for resolution) are connected by a shared singular variety, $X_0$, with nodal singularities. From $X_0$ the singularities can be smoothed by deformation of complex structure (corresponding to increasing non-trivial $S^3$ cycles from zero size) to obtain $X_D$. A small resolution of the singular geometry (by replacing the singular points with curves that are topologically $\mathbb{P}^1$s) results in $X_R$.
• Figure 2: A schematic of the intersection of the deformation and resolution manifolds in a Calabi-Yau conifold transition, described in a shared ambient space.