Singular Geometry and Higgs Bundles in String Theory

Abstract

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 of physical interactions, it has opened the door to the geometric engineering of many physical systems, and in particular those involving Higgs bundles. This note presents a curated overview of some current advances and open problems in the area, with no intention of being a complete review of the whole subject.

References in corpus (27)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• 6d Conformal Matter
• T-Branes and Monodromy
• 6D SCFTs and Phases of 5D Theories
• Mordell-Weil Torsion and the Global Structure of Gauge Groups in F-theory
• Geometric constraints in dual F-theory and heterotic string compactifications
• A New Model for Elliptic Fibrations with a Rank One Mordell-Weil Group: I. Singular Fibers and Semi-Stable Degenerations
• Gauge Theory And Wild Ramification
• Spectral data for G-Higgs bundles
• Asymptotic Geometry of the Hitchin Metric
• Cayley and Langlands type correspondences for orthogonal Higgs bundles
• Compact T-branes
• The Geometry of G${}_2$, Spin(7), and Spin(8)-models
• On the image of the parabolic Hitchin map
• The Geometry of F${}_4$-Models
• Involutions of the moduli spaces of $G$-Higgs bundles over elliptic curves
• Box Graphs and Resolutions I
• T-branes and Matrix Models
• From $S^1$-fixed points to $\mathcal{W}$-algebra representations
• Higgs bundles, Lagrangians and mirror symmetry
• Branes on the singular locus of the Hitchin system via Borel and other parabolic subgroups
• Intermediate Jacobians and ADE Hitchin Systems
• SO(n,n+1)-surface group representations and their Higgs bundles
• Mirror symmetry for Nahm branes
• Cameral data for SU(p+1,p)-Higgs bundles
• Positivity and higher Teichmüller theory
• S-duality of boundary conditions and the Geometric Langlands program

Cited by in corpus (12)

• Flopping and Slicing: SO(4) and Spin(4)-models
• Mordell-Weil Torsion, Anomalies, and Phase Transitions
• Unramified covers and branes on the Hitchin system
• The Geometry of SO(3), SO(5), and SO(6) models
• 48 Crepant Paths to $\text{SU}(2)\times \text{SU}(3)$
• Heterotic/Heterotic and Heterotic/F-theory Duality
• Perspectives on the Asymptotic Geometry of the Hitchin Moduli Space
• Extending the Geometry of Heterotic Spectral Cover Constructions
• Higgs bundles -- Recent applications
• The suspended pinch point and SU($2$)$\times$U($1$) gauge theories
• Aspects of Calabi-Yau Integrable and Hitchin Systems
• Parabolic Higgs bundles, $t{t}^{\ast }$ connections and opers