String Modular Phases in Calabi-Yau Families

Abstract

We investigate the structure of singular Calabi-Yau varieties in moduli spaces that contain a Brieskorn-Pham point. Our main tool is a construction of families of deformed motives over the parameter space. We analyze these motives for general fibers and explicitly compute the $L-$series for singular fibers for several families. We find that the resulting motivic $L-$functions agree with the $L-$series of modular forms whose weight depends both on the rank of the motive and the degree of the degeneration of the variety. Surprisingly, these motivic $L-$functions are identical in several cases to $L-$series derived from weighted Fermat hypersurfaces. This shows that singular Calabi-Yau spaces of non-conifold type can admit a string worldsheet interpretation, much like rational theories, and that the corresponding irrational conformal field theories inherit information from the Gepner conformal field theory of the weighted Fermat fiber of the family. These results suggest that phase transitions via non-conifold configurations are physically plausible. In the case of severe degenerations we find a dimensional transmutation of the motives. This suggests further that singular configurations with non-conifold singularities may facilitate transitions between Calabi-Yau varieties of different dimensions.

34 pages

References in corpus (4)

• Dynamical compactification from de Sitter space
• Transdimensional Tunneling in the Multiverse
• The Langlands Program and String Modular K3 Surfaces
• A family of SCFTs hosting all "very attractive" relatives of the (2)^4 Gepner model

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• String Automorphic Motives of nondiagonal Varieties
• Automorphic Black Hole Entropy
• Black Hole Probes of Automorphic Space
• Motivic L-Function Identities from CFT and Arithmetic Mirror Symmetry
• K-Rational D-Brane Crystals
• Emergent spacetime and black hole probes from automorphic forms