# Singular Geometry and Higgs Bundles in String Theory

@article{Anderson2017SingularGA, title={Singular Geometry and Higgs Bundles in String Theory}, author={Lara B. Anderson and Laura Fredrickson and Mboyo Esole and Laura P. Schaposnik}, journal={Symmetry Integrability and Geometry-methods and Applications}, year={2017}, volume={14}, pages={037} }

This brief survey aims to set the stage and summarize some of the ideas under discussion at the Workshop on Singular Geometry and Higgs Bundles in String Theory, to be held at the American Institute of Mathematics from October 30th to November 3rd, 2017. One of the most interesting aspects of the duality revolution in string theory is the understanding that gauge fields and matter representations can be described by intersection of branes. Since gauge theory is at the heart of our description…

## 27 Citations

### Advanced topics in gauge theory: Mathematics and Physics of Higgs bundles

- MathematicsQuantum Field Theory and Manifold Invariants
- 2021

These notes have been prepared as reading material for the mini-course given by the author at the "2019 Graduate Summer School" at Park City Mathematics Institute - Institute for Advanced Study. We…

### Torsion line bundles and branes on the Hitchin system

- Mathematics
- 2018

We study the fixed loci for the action of tensorisation by a line bundle of order $n$ on the moduli space of Higgs bundles for the Langlands self-dual group $\mathrm{GL}(n,\mathbb{C})$. We equip…

### Mirror symmetry for Nahm branes

- MathematicsÉpijournal de Géométrie Algébrique
- 2022

The Dirac--Higgs bundle is a hyperholomorphic bundle over the moduli space of
stable Higgs bundles of coprime rank and degree. We provide an algebraic
generalization to the case of trivial degree and…

### The suspended pinch point and SU(2)×U(1) gauge theories

- Mathematics
- 2019

We show that the suspended pinch point can be seen as an elliptically fibered variety with singular fibers of type I2 over codimension-one points of the base and a torsionless Mordell–Weil group of…

### T-branes and defects

- MathematicsJournal of High Energy Physics
- 2019

A bstractWe study T-branes on compact Kähler surfaces, in the presence of fields localised at curves. If such fields are treated as defects, their vevs induce delta-function sources for the 7-brane…

### The two faces of T-branes

- MathematicsJournal of High Energy Physics
- 2019

We establish a brane-brane duality connecting T-branes to collections of ordinary D-branes. T-branes are intrinsically non-Abelian brane configurations with worldvolume flux, whereas their duals…

### USp(4)-models

- Mathematics
- 2019

We study the geometry of elliptic fibrations satisfying the conditions of Step 2 of Tate's algorithm with a discriminant of valuation 4. We call such geometries USp(4)-models, as the dual graph of…

### Mordell-Weil Torsion, Anomalies, and Phase Transitions

- Mathematics
- 2017

We explore how introducing a non-trivial Mordell-Weil group changes the structure of the Coulomb phases of a five-dimensional gauge theory from an M-theory compactified on an elliptically fibered…

### Flopping and Slicing: SO(4) and Spin(4)-models

- Mathematics
- 2018

We study the geometric engineering of gauge theories with gauge group Spin(4) and SO(4) using crepant resolutions of Weierstrass models. The corresponding elliptic fibrations realize a collision of…

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