Evidence for F(uzz) theory

Jonathan J. Heckman, Herman Verlinde

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


We show that in the decoupling limit of an F-theory compactification, the internal directions of the seven-branes must wrap a non-commutative four-cycle S. We introduce a general method for obtaining fuzzy geometric spaces via toric geometry and develop tools for engineering four-dimensional GUT models from this non-commutative setup. We obtain the chiral matter content and Yukawa couplings, and show that the theory has a finite Kaluza-Klein spectrum. The value of 1/αgut is predicted to be equal to the number of fuzzy points on the internal four-cycle S. This relation puts a non-trivial restriction on the space of gauge theories that can arise as a limit of F-theory. By viewing the seven-brane as tiled by D3-branes sitting at the N fuzzy points of the geometry we argue that this theory admits a holographic dual description in the large N limit. We also entertain the possibility of constructing string models with large fuzzy extra dimensions, but with a high scale for quantum gravity.

Original languageEnglish (US)
Article number44
JournalJournal of High Energy Physics
Issue number1
StatePublished - 2011

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • F-theory
  • Non-commutative geometry


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