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 \( \mathcal{S} \). 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/α GUT is predicted to be equal to the number of fuzzy points on the internal four-cycle \( \mathcal{S} \). 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.
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Heckman, J.J., Verlinde, H. Evidence for F(uzz) theory. J. High Energ. Phys. 2011, 44 (2011). https://doi.org/10.1007/JHEP01(2011)044
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DOI: https://doi.org/10.1007/JHEP01(2011)044