We use deep autoencoder neural networks to draw a chart of the heterotic Z 6 -II orbifold landscape. Even though the autoencoder is trained without knowing the phenomenological properties of the Z 6 -II orbifold models, it identifies fertile islands in this chart where phenomenologically promising models cluster. Then, we apply a decision tree to our chart in order to extract the defining properties of the fertile islands. Based on this information we propose a new search strategy for phenomenologically promising string models.
We investigate under which conditions the cosmological constant vanishes perturbatively at the oneloop level for heterotic strings on non-supersymmetric toroidal orbifolds. To obtain model-independent results, which do not rely on the gauge embedding details, we require that the right-moving fermionic partition function vanishes identically in every orbifold sector. This means that each sector preserves at least one, but not always the same Killing spinor. The existence of such Killing spinors is related to the representation theory of finite groups, i.e. of the point group that underlies the orbifold. However, by going through all inequivalent (Abelian and non-Abelian) point groups of six-dimensional toroidal orbifolds we show that this is never possible: For any non-supersymmetric orbifold there is always (at least) one sector, that does not admit any Killing spinor. The underlying mathematical reason for this no-go result is formulated in a conjecture, which we have tested by going through an even larger number of finite groups. This conjecture could be applied to situations beyond symmetric toroidal orbifolds, like asymmetric orbifolds.
We apply techniques from data mining to the heterotic orbifold landscape in order to identify new MSSM-like string models. To do so, so-called contrast patterns are uncovered that help to distinguish between areas in the landscape that contain MSSM-like models and the rest of the landscape. First, we develop these patterns in the well-known Z 6 -II orbifold geometry and then we generalize them to all other Z N orbifold geometries. Our contrast patterns have a clear physical interpretation and are easy to check for a given string model. Hence, they can be used to scale down the potentially interesting area in the landscape, which significantly enhances the search for MSSM-like models. Thus, by deploying the knowledge gain from contrast mining into a new search algorithm we create many novel MSSM-like models, especially in corners of the landscape that were hardly accessible by the conventional search algorithm, for example, MSSM-like Z 6 -II models with ∆(54) flavor symmetry.
MSSM-like string models from the compactification of the heterotic string on toroidal orbifolds (of the kind 6 ∕P) have distinct phenomenological properties, like the spectrum of vector-like exotics, the scale of supersymmetry breaking, and the existence of non-Abelian flavor symmetries. We show that these characteristics depend crucially on the choice of the underlying orbifold point group P. In detail, we use boosted decision trees to predict P from phenomenological properties of MSSM-like orbifold models. As this works astonishingly well, we can utilize machine learning to predict the orbifold origin of the MSSM.
We investigate under which conditions the cosmological constant vanishes perturbatively at the one‐loop level for heterotic strings on non‐supersymmetric toroidal orbifolds. To obtain model‐independent results, which do not rely on the gauge embedding details, we require that the right‐moving fermionic partition function vanishes identically in every orbifold sector. This means that each sector preserves at least one, but not always the same Killing spinor. The existence of such Killing spinors is related to the representation theory of finite groups, i.e. of the point group that underlies the orbifold. However, by going through all inequivalent (Abelian and non‐Abelian) point groups of six‐dimensional toroidal orbifolds we show that this is never possible: For any non‐supersymmetric orbifold there is always (at least) one sector, that does not admit any Killing spinor. The underlying mathematical reason for this no‐go result is formulated in a conjecture, which we have tested by going through an even larger number of finite groups. This conjecture could be applied to situations beyond symmetric toroidal orbifolds, like asymmetric orbifolds.
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