Intersection Theory on Weighted Blowups of F-theory Vacua

Apr 29, 2023
44 pages
e-Print:
Report number:
  • MIT-CTP-5551

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Abstract: (arXiv)
Generalizing the results of 1211.6077 and 1703.00905, we prove a formula for the pushforward of an arbitrary analytic function of the exceptional divisor class of a weighted blowup of an algebraic variety centered at a smooth complete intersection with normal crossing. We check this formula extensively by computing the generating function of intersection numbers of a weighted blowup of the generic SU(5) Tate model over arbitrary smooth base, and comparing the answer to known results. Motivated by applications to four-dimensional F-theory flux compactifications, we use our formula to compute the intersection pairing on the vertical part of the middle cohomology of elliptic Calabi-Yau 4-folds resolving the generic F4_4 and Sp(6) Tate models with non-minimal singularities. These resolutions lead to non-flat fibrations in which certain fibers contain 3-fold (divisor) components, whose physical interpretation in M/F-theory remains to be fully explored.
Note:
  • 37 pages plus an appendix. v2: Minor clarifications to Sections 3 and 4
  • compactification: flux
  • F-theory
  • space: Calabi-Yau
  • algebra
  • cohomology
  • vacuum state: flux
  • singularity
  • fibre bundle
  • SU(5)