Hilbert functions of Koszul maps turn empirical chamber-wise polynomial formulae for line bundle cohomology on CICY threefolds into explicit analytic or finite-box certified statements.
(MS)SM-like models on smooth Calabi-Yau manifolds from all three heterotic string theories
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abstract
We perform model searches on smooth Calabi-Yau compactifications for both the supersymmetric E8xE8 and SO(32) as well as for the non-supersymmetric SO(16)xSO(16) heterotic strings simultaneously. We consider line bundle backgrounds on both favorable CICYs with relatively small h_11 and the Schoen manifold. Using Gram matrices we systematically analyze the combined consequences of the Bianchi identities and the tree-level Donaldson-Uhlenbeck-Yau equations inside the Kahler cone. In order to evaluate the model building potential of the three heterotic theories on the various geometries, we perform computer-aided scans. We have generated a large number of GUT-like models (up to over a few hundred thousand on the various geometries for the three heterotic theories) which become (MS)SM-like upon using a freely acting Wilson line. For all three heterotic theories we present tables and figures summarizing the potentially phenomenologically interesting models which were obtained during our model scans.
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hep-th 1years
2026 1verdicts
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Hilbert Functions and Line Bundle Cohomology on CICY Threefolds
Hilbert functions of Koszul maps turn empirical chamber-wise polynomial formulae for line bundle cohomology on CICY threefolds into explicit analytic or finite-box certified statements.