Statistics of limit root bundles relevant for exact matter spectra of F-theory MSSMs
In the largest, currently known, class of one quadrillion globally consistent F-theory Standard Models with gauge coupling unification and no chiral exotics, the vectorlike spectra are counted by cohomologies of root bundles. In this work, we apply a previously proposed method to identify toric base threefolds, which are promising to establish F-theory Standard Models with exactly three quark doublets and no vectorlike exotics in this representation. The base spaces in question are obtained from triangulations of 708 polytopes. By studying root bundles on the quark-doublet curve Cð3;2Þ1=6 and employing well-known results about desingularizations of toric K3 surfaces, we derive a triangulation independent lower bound Nˇ ð3Þ P for the number Nð3Þ P of root bundles on Cð3;2Þ1=6 with exactly three sections. The ratio Nˇ ð3Þ P =NP, where NP is the total number of roots on Cð3;2Þ1=6 , is largest for base spaces associated with triangulations of the eighth three-dimensional polytope Δ∘ 8 in the Kreuzer-Skarke list. For each of these Oð1015Þ threefolds, we expect that many root bundles on Cð3;2Þ1=6 are induced from F-theory gauge potentials and that at least every 3000th root on Cð3;2Þ1=6 has exactly three global sections and thus no exotic vectorlike quark-doublet modes.
2021
2023-10-13 15:37:42
1033
astrophysics, compactification, string theory models, geometry, higher-dimensional field theories, mathematical physics, quantum fields in curved spacetime, string phenomenology, supersymmetric models, topology
astrofizika, modeli teorije strun, geometrija, teorije polja, matematična fizika, kvantna polja v ukrivljenem prostor-času, fenomenologija strun, supersimetrični modeli, topologija
r2
American Physical Society
Martin
Bies
70
Mirjam
Cvetič
70
Mingqiang
Liu
70
UDK
4
52
COBISS_ID
3
97892611
ISSN pri članku
9
2470-0029
Statistics_of_limit_root_Bies_2021bundles.pdf
454790
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2023-10-13 15:50:52
0
Izvorni URL
2023-10-13 15:37:56