Brill-Noether-general limit root bundles: absence of vector-like exotics in F-theory Standard Models

Root bundles appear prominently in studies of vector-like spectra of 4d F-theory compactifications. Of particular importance to phenomenology are the Quadrillion F-theory Standard Models (F-theory QSMs). In this work, we analyze a superset of the physical root bundles whose cohomologies encode the vector-like spectra for the matter representations ( 3 , 2 ) 1 / 6 , ( 3 , 1 ) − 2 / 3 and ( 1 , 1 ) 1 . For the family B 3 ( Δ_4^^∘ ) consisting of 𝒪 (10 11 ) F-theory QSM geometries, we argue that more than 99 . 995