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arXiv · 2606.27490

Free-Field Construction of Heterotic String Compactified on Calabi-Yau Orbifolds via Correspondence with $\mathcal{N}{=}2$ SCFT Minimal Models

Alexander Belavin·Doron Gepner·Grigory Makarov
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Abstract

We establish a correspondence between the free-field construction and the minimal-model construction of the Calabi--Yau sector of the four-dimensional heterotic string compactified on Berglund--H\"{u}bsch type Calabi--Yau manifolds and their orbifolds. For Fermat-type polynomials the Calabi--Yau vertex operators expressed in terms of free fields are shown to correspond to products of primary fields of $\mathcal{N}{=}2$ minimal models. Using this correspondence we verify modular invariance of the free-field construction and extend it to Berglund--H\"{u}bsch Calabi--Yau orbifolds, deriving the conditions on complete vertex operators that parallel those of the minimal-model construction.

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Alexander Belavin, Doron Gepner, Grigory Makarov. 2026-06-25. Free-Field Construction of Heterotic String Compactified on Calabi-Yau Orbifolds via Correspondence with $\mathcal{N}{=}2$ SCFT Minimal Models. https://arxiv.org/abs/2606.27490

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