Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 037, 27 pages      arXiv:1710.08453      https://doi.org/10.3842/SIGMA.2018.037

Singular Geometry and Higgs Bundles in String Theory

Lara B. Anderson a, Mboyo Esole b, Laura Fredrickson c and Laura P. Schaposnik de
a) Department of Physics and Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, USA
b) Department of Mathematics, Northeastern University, Boston, MA 02115, USA
c) Department of Mathematics, Stanford University, Stanford, CA 94305, USA
d) Department of Mathematics, University of Illinois at Chicago, 60607 Chicago, USA
e) Department of Mathematics, FU Berlin, 14195 Berlin, Germany

Received November 22, 2017, in final form April 13, 2018; Published online April 18, 2018

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.

Key words: Higgs bundles; Hitchin fibration; mirror symmetry; F-theory; Calabi-Yau; singular curves; singularities.

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