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F-theory on singular spaces

Andres Collinucci, Raffaele Savelli

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.

F-theory on singular spaces

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.

Paper Structure

This paper contains 13 sections, 82 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Introduction to matrix factorizations
  3. Basic definitions
  4. Relation to D7-branes
  5. Knörrer's periodicity
  6. F-theory on singularities
  7. The affine case
  8. Chiral gluing modes
  9. A class of compact models
  10. Global T-branes and point-like matter
  11. Matrix factorizations vs resolutions
  12. Breaking patterns and obstructions to blow-up
  13. Discussion

Figures (4)

  • Figure 1: Two parallel D6-branes. The blue strings uplift to moduli of two-centered Taub-NUT metric, whereas the red string uplifts to a 'vanishing' M2-brane.
  • Figure 2: Two intersecting D7-branes lifting to a conifold geometry, resulting from the collision of two families of Taub-NUT spaces. The red string uplifts to a 'vanishing' M2-brane at the tip of the conifold.
  • Figure 3: Schematic picture of a multi-centered Taub-NUT space.
  • Figure 4: Auslander-Reiten quiver for an A$_{n-1}$ singularity