20.500.12556/DKUM-86157 Root bundles and towards exact matter spectra of F-theory MSSMs Motivated by the appearance of fractional powers of line bundles in studies of vector-like spectra in 4d F-theory compactifications, we analyze the structure and origin of these bundles. Fractional powers of line bundles are also known as root bundles and can be thought of as generalizations of spin bundles. We explain how these root bundles are linked to inequivalent F-theory gauge potentials of a G(4)-flux. While this observation is interesting in its own right, it is particularly valuable for F-theory Standard Model constructions. In aiming for MSSMs, it is desired to argue for the absence of vector-like exotics. We work out the root bundle constraints on all matter curves in the largest class of currently-known F-theory Standard Model constructions without chiral exotics and gauge coupling unification. On each matter curve, we conduct a systematic "bottom"-analysis of all solutions to the root bundle constraints and all spin bundles. Thereby, we derive a lower bound for the number of combinations of root bundles and spin bundles whose cohomologies satisfy the physical demand of absence of vector-like pairs. On a technical level, this systematic study is achieved by a well-known diagrammatic description of root bundles on nodal curves. We extend this description by a counting procedure, which determines the cohomologies of so-called limit root bundles on full blow-ups of nodal curves. By use of deformation theory, these results constrain the vector-like spectra on the smooth matter curves in the actual F-theory geometry. F-theory differential geometry algebraic geometry F teorija diferencialna geometrija algebrska geometrija true false true SISSA Angleški jezik Slovenski jezik Znanstveno delo 2023-10-13 16:01:08 2023-10-16 09:06:09 2023-10-17 03:10:21 0000-00-00 00:00:00 2021 0 0 II, 63 str. Št. 9, št. članka 76 23. sep. 2021 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2021-04-16 2021-08-25 2021-09-14 517:52 97935875 10.1007/JHEP09(2021)076 1029-8479 Root_bundles_andtowards_exact_matter_spectra_Bies_2021.pdf Root_bundles_andtowards_exact_matter_spectra_Bies_2021.pdf 1 F20F6A9895D2D8ED69EBBE4B5F880B54 2177540076c36c2db9ed4c7b1707c4816ba48e3a0e980287181a4206abd127d0 093d5f8d-69d1-11ee-b6cb-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=173565 https://link.springer.com/article/10.1007/JHEP09(2021)076 0 fc3d53ff-69d0-11ee-b6cb-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=173564 Univerza v Mariboru 0 0 0