## Abstract

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 language | English (US) |
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Article number | 44 |

Journal | Journal of High Energy Physics |

Volume | 2011 |

Issue number | 1 |

DOIs | |

State | Published - 2011 |

## All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

## Keywords

- F-theory
- Non-commutative geometry