F-theory on singular spaces

TL;DR

This paper introduces a new framework for analyzing F-theory on singular spaces directly using matrix factorizations, enabling exploration of exotic gauge sectors like T-branes in a global setting.

Contribution

It presents a novel approach to study F-theory on singular geometries without resolution, expanding the understanding of gauge theories and bound states such as T-branes.

Findings

Demonstrates the use of Eisenbud's matrix factorizations for hypersurface singularities.

Provides examples including conifold and orbifold singularities.

Applies the method to compact elliptically fibered Calabi-Yau fourfolds.

Abstract

We propose a framework for treating F-theory directly, without resolving or deforming its singularities. This allows us to explore new sectors of gauge theories, including exotic bound states such as T-branes, in a global context. We use the mathematical framework known as Eisenbud's matrix factorizations for hypersurface singularities. We display the usefulness of this technique by way of examples, including affine singularities of both conifold and orbifold type, as well as a class of full-fledged compact elliptically fibered Calabi-Yau fourfolds.