Twisted Fibrations in M/F-theory

In this work we investigate 5-dimensional theories obtained from M-theory on genus one fibered threefolds which exhibit twisted algebras in their fibers. We provide a base-independent algebraic description of the threefolds and compute light 5D BPS states charged under finite sub-algebras of the twisted algebras. We further construct the Jacobian fibrations that are associated to 6-dimensional F-theory lifts, where the twisted algebra is absent. These 6/5-dimensional theories are compared via twisted circle reductions of F-theory to M-theory. In the 5-dimensional theories we discuss several geometric transitions that connect twisted with untwisted fibrations. We present detailed discussions of e(6)((2)), so(8)((3)) and su(3)((2)) twisted fibers and provide several explicit example threefolds via toric constructions. Finally, limits are considered in which gravity is decoupled, including Little String Theories for which we match 2-group symmetries across twisted T-dual theories.