Evidence for F(uzz) Theory

TL;DR

This paper demonstrates that in F-theory compactifications, seven-branes wrap non-commutative four-cycles, introduces fuzzy geometry methods for model building, and predicts a relation between GUT coupling and fuzzy points, with implications for holography and string models.

Contribution

It develops a general framework for fuzzy geometries in F-theory, enabling the construction of GUT models with finite spectra and novel geometric restrictions.

Findings

Finite Kaluza-Klein spectrum in non-commutative setup

Relation between GUT coupling and number of fuzzy points

Holographic dual description in large N limit

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/alpha_(GUT) 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.