Singular Geometry and Higgs Bundles in String Theory

  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},
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… 

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

  • L. Schaposnik
  • Mathematics
    Quantum 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

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

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

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

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

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


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

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

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



T-branes at the limits of geometry

A bstractSingular limits of 6D F-theory compactifications are often captured by T-branes, namely a non-abelian configuration of intersecting 7-branes with a nilpotent matrix of normal deformations.

Geometry of the moduli space of Higgs bundles

This thesis contains work which appeared in several papers. Additionally to the results in the papers it contains a detailed introduction and some further proofs and remarks. The dissertation gives a

Gluing branes — I

A bstractWe consider several aspects of holomorphic brane configurations. We recently showed that an important part of the defining data of such a configuration is the gluing morphism, which

T-branes and geometry

A bstractT-branes are a non-abelian generalization of intersecting branes in which the matrix of normal deformations is nilpotent along some subspace. In this paper we study the geometric remnant of

Gluing branes — II: flavour physics and string duality

  • Ron DonagiMartijn Wijnholt
  • Physics
  • 2011
A bstractRecently we discussed new aspects of degenerate brane configurations, which can appear in the context of heterotic strings, perturbative type II, or M/F-theory. Here we continue our study of

Spinors, Lagrangians and rank 2 Higgs bundles

This article considers the Dirac operator on a Riemann surface coupled to a symplectic holomorphic vector bundle W . Each spinor in the null‐space (which is a holomorphic section of W⊗K1/2 )

Higgs bundles, Lagrangians and mirror symmetry

Let Σ be a compact Riemann surface of genus g ≥ 2. This thesis is dedicated to the study of certain loci of the Higgs bundle moduli space. After recalling basic facts in the first chapter about

Ends of the moduli space of Higgs bundles

We associate to each stable Higgs pair (A(0), Phi(0)) on a compact Riemann surface X a singular limiting configuration (A(infinity), Phi(infinity)), assuming that det Phi has only simple zeroes. We

Matter and singularities

A bstractWe analyze the structure of matter representations arising from codimension two singularities in F-theory, focusing on gauge groups SU(N). We give a detailed local description of the