Twisted Fibrations in M/F-theory

TL;DR

This paper explores 5D theories from M-theory on genus one fibered threefolds with twisted fibers, analyzing their algebraic structures, BPS states, and connections to 6D F-theory, revealing new geometric and physical insights.

Contribution

It provides a base-independent algebraic description of twisted threefolds, constructs associated Jacobian fibrations, and compares twisted and untwisted theories via geometric transitions and dualities.

Findings

Computed light 5D BPS states charged under twisted algebras

Constructed Jacobian fibrations for 6D F-theory lifts

Analyzed geometric transitions connecting twisted and untwisted fibrations

Abstract

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 $\mathfrak{e}_6^{(2)}, \mathfrak{so}_8^{(3)}$ and $\mathfrak{su}_3^{(2)}$ 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.