The complete massless singlet spectrum in the free-field construction of heterotic strings on Calabi–Yau orbifolds
Year: 2026
Type: article
Abstract: A bstract We apply the free-field construction of the heterotic string compactified on Berglund–Hübsch Calabi–Yau orbifolds by computing the full spectrum of massless E 6 singlets. The contribution of the descendant vertices is obtained by combining the exact content of the irreducible N = 2 minimal model representations, encoded in the ranks of the Shapovalov matrices, with the twisted sector structure of the orbifold. The method reproduces the known spectrum of the quintic orbifold with Hodge numbers (17, 21), namely 17 generations, 21 antigenerations and 234 singlets. For the quintic itself we obtain 330 singlets. We show that this number, rather than the frequently quoted value 326, obtained from the geometric description, is the correct one at the Gepner point, in agreement with the Landau–Ginzburg computation of Kachru and Witten. We also provide an explicit construction of the general vertices. We then compute the new spectra of the two remaining quintic orbifolds, Z 5 [0, 1, 2, 3, 4] with (21, 1, 210) and Z 5 [0, 0, 0, 1, 4] with (49, 5, 258), where the exceptional Hodge number h 2,1 = 49 arises from the twisted sectors. All four examples satisfy exact mirror-symmetry checks.
Source: Journal of High Energy Physics
Author: Vladimir Belavin
Institution: Ariel University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7170043399
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