20.500.12556/DKUM-86156 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. 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 true false true American Physical Society Angleški jezik Slovenski jezik Znanstveno delo 2023-10-13 15:37:42 2023-10-16 08:53:24 2024-08-07 10:08:14 0000-00-00 00:00:00 2021 0 0 Str. 1-8 Št. 6, št. članka L061903 Letn. 104 15. sep. 2021 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2021-05-24 2021-07-13 2021-09-15 52 97892611 2470-0029 Statistics_of_limit_root_Bies_2021bundles.pdf Statistics_of_limit_root_Bies_2021bundles.pdf 1 8E899AB54C5BDEA48C45F36E4EEAB70B 2b0c15826c0a7992c9ec0597b8b1f76aa3878b412eaaf07fd58daad48239eff9 85d915db-69cf-11ee-b6cb-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=173563 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.104.L061903 0 b6def199-69cd-11ee-b6cb-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=173562 Univerza v Mariboru 0 0 0