Weak coupling, degeneration and log Calabi-Yau spaces

Ron Donagi, Sheldon Katz, Martijn Wijnholt

Research output: Contribution to journalArticlepeer-review


We establish a new weak coupling limit in F-theory. The new limit may be thought of as the process in which a local model bubbles off from the rest of the Calabi-Yau. The construction comes with a small deformation parameter t such that computations in the local model become exact as t → 0. More generally, we advocate a modular approach where compact Calabi-Yau geometries are obtained by gluing together local pieces (log Calabi-Yau spaces) into a normal crossing variety and smoothing, in analogy with a similar cutting and gluing approach to topological field theories. We further argue for a holographic relation between F-theory on a degenerate Calabi-Yau and a dual theory on its boundary, which fits nicely with the gluing construction.

Original languageEnglish (US)
Pages (from-to)665-738
Number of pages74
JournalPure and Applied Mathematics Quarterly
Issue number4
StatePublished - 2013


  • Calabi-Yau
  • Elliptic fibration
  • F-theory
  • Semi-stable degeneration
  • Smoothing
  • String compactification
  • Variation of hodge structure

ASJC Scopus subject areas

  • Mathematics(all)


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