F-theory, SO(32) and Toric Geometry

TL;DR

This paper explores the duality between F-theory and heterotic string theories with different gauge symmetries, utilizing toric geometry and polyhedra to identify and construct large gauge groups in various dimensions.

Contribution

It introduces a generalized concept of 'tops' in toric geometry, enabling the construction of new large gauge groups in F-theory compactifications.

Findings

Reproduced the 'record gauge group' in six dimensions.

Constructed a new 'record gauge group' in four dimensions.

Linked F-theory duals to heterotic strings using polyhedral descriptions.

Abstract

We show that the F-theory dual of the heterotic string with unbroken Spin(32)/Z_2 symmetry in eight dimensions can be described in terms of the same polyhedron that can also encode unbroken E_8\times E_8 symmetry. By considering particular compactifications with this K3 surface as a fiber, we can reproduce the recently found `record gauge group' in six dimensions and obtain a new `record gauge group' in four dimensions. Our observations relate to the toric diagram for the intersection of components of degenerate fibers and our definition of these objects, which we call `tops', is more general than an earlier definition by Candelas and Font.