Tate’s algorithm and F-theory

  • Sheldon Katz
  • David R. Morrison
  • Sakura Schäfer-Nameki
  • James Sully


The “Tate forms” for elliptically fibered Calabi-Yau manifolds are reconsidered in order to determine their general validity. We point out that there were some implicit assumptions made in the original derivation of these “Tate forms” from the Tate algorithm. By a careful analysis of the Tate algorithm itself, we deduce that the “Tateforms” (without any futher divisiblity assumptions) do not hold in some instances and have to be replaced by a new type of ansatz. Furthermore, we give examples in which the existence of a “Tate form” can be globally obstructed, i.e., the change of coordinates does not extend globally to sections of the entire base of the elliptic fibration. These results have implications both for model-building and for the exploration of the landscape of F-theory vacua.


F-Theory D-branes 


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Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  • Sheldon Katz
    • 1
  • David R. Morrison
    • 2
    • 3
    • 4
  • Sakura Schäfer-Nameki
    • 5
    • 6
  • James Sully
    • 3
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaU.S.A.
  2. 2.Department of MathematicsUniversity of CaliforniaSanta BarbaraU.S.A.
  3. 3.Department of PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  4. 4.Institute for the Physics and Mathematics of the UniverseUniversity of TokyoKashiwaJapan
  5. 5.Kavli Institute for Theoretical PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  6. 6.Department of Mathematics, King’s CollegeUniversity of LondonLondonU.K.

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