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Singular geometry and Higgs bundles in string theory. (English) Zbl 1419.14016

This is a well-described review of current advances and open problems for the Higgs bundles in the string theory.
Authors’ 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.”

MSC:

14D20 Algebraic moduli problems, moduli of vector bundles
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
14H70 Relationships between algebraic curves and integrable systems
14P25 Topology of real algebraic varieties
14J33 Mirror symmetry (algebro-geometric aspects)
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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References:

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