F-theory on Quotient Threefolds with (2,0) Discrete Superconformal Matter

TL;DR

This paper investigates F-theory compactifications on quotient threefolds with (2,0) superconformal matter, revealing geometric transitions that connect different Calabi-Yau geometries and involve discrete gauge symmetries and non-trivial matter couplings.

Contribution

It introduces new geometric constructions and transitions in F-theory compactifications with (2,0) superconformal matter, including Higgsing to discrete symmetries and hyperconifold transitions.

Findings

Demonstrates Higgsing from U(1) to discrete gauge symmetry with superconformal matter

Constructs geometric transitions linking different Calabi-Yau threefolds

Identifies hyperconifold transitions with multiple fibers in co-dimension 2

Abstract

We explore 6-dimensional compactifications of F-theory exhibiting (2,0) superconformal theories coupled to gravity that include discretely charged superconformal matter. Beginning with F-theory geometries with Abelian gauge fields and superconformal sectors, we provide examples of Higgsing transitions which break the $U(1)$ gauge symmetry to a discrete remnant in which the matter fields are also non-trivially coupled to a (2,0) SCFT. In the compactification background this corresponds to a geometric transition linking two fibered Calabi-Yau geometries defined over a singular base complex surface. An elliptically fibered Calabi-Yau threefold with non-zero Mordell-Weil rank can be connected to a smooth non-simply connected genus one fibered geometry constructed as a Calabi-Yau quotient. These hyperconifold transitions exhibit multiple fibers in co-dimension 2 over the base.