Fabian Ruehle

About Me
Fabian Ruehle
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Flops for Complete Intersection Calabi-Yau Threefolds

branched double cover

GTP formula

We discuss flops in projective Complete Intersection Calabi-Yau manifolds. We explain that there are two different types of flops, whose presence and type can be read off from the GLSM charges. Of course, this can also be used to engineer manifolds that exhibit a certain flop type.
Case 1: A GLSM U(1) charge contains only 0's and 1's. This signals the presence of flops to non-isomorphic manifolds.
Case 2: A GLSM U(1) charge contains a single 2, followed by 0's and 1's. This signals the presence of flops to isomorphic manifolds.
We explain in both cases how to describe the manifold as well as the singular manifold that sits in between two flops. These require moving away from projective CICYs to more general toric models, determinantal varieties (for case 1), or more complicated manifolds (in the second case). As shown in the figure, these are small resolutions of branched double covers of the "base".
We also explain how to describe the flopped divisors (and in fact the isomorphism of the Picard groups) under both types of flops. We also explain how to get the number of contracted curves in the flop from either comparing the Euler characteristic or by using the Giambelli-Thom-Porteous formula (see bottom figure for an example).


Tuesdays: Jointly with colleagues from the String Pheno community, I am organizing the weekly String Pheno seminar series.

Wednesdays: Jointly with scientists from academia (Madison, Munich, Northeastern) and industry (Deepmind, Google Brain, Microsoft), I am organizing the bi-weekly seminar series Physics meets ML.

Physics Report

I have written a Physics Report on Data science applications to string theory. It comes with a Github repo.