Geometric Singularities and Enhanced Gauge Symmetries
M. Bershadsky, K. Intriligator, S. Kachru, D.R. Morrison, V. Sadov,, and C. Vafa
TL;DR
This paper uses Tate's algorithm to identify loci of enhanced gauge symmetry in F-theory compactifications, testing dualities, and discovering new gauge symmetry enhancements, with implications for string theory dualities and Calabi-Yau geometries.
Contribution
It applies Tate's algorithm to analyze gauge symmetry enhancements in F-theory and explores their dualities with heterotic strings, revealing new mixed perturbative and non-perturbative phenomena.
Findings
Recovered perturbative gauge symmetry enhancements in heterotic duals
Discovered new mixed perturbative/non-perturbative gauge symmetry enhancements
Derived Calabi-Yau threefolds dual to heterotic Coulomb branches
Abstract
Using ``Tate's algorithm,'' we identify loci in the moduli of F-theory compactifications corresponding to enhanced gauge symmetry. We apply this to test the proposed F-theory/heterotic dualities in six dimensions. We recover the perturbative gauge symmetry enhancements of the heterotic side and the physics of small instantons, and discover new mixed perturbative/non-perturbative gauge symmetry enhancements. Upon further toroidal compactification to 4 dimensions, we derive the chain of Calabi-Yau threefolds dual to various Coulomb branches of heterotic strings.
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