A brief survey of Higgs bundles

 

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Bibliographic Details
Author: Zúñiga Rojas, Ronald Alberto
Format: artículo original
Publication Date:2019
Description:Considering a compact Riemann surface of genus greater or equal than two, a Higgs bundle is a pair composed of a holomorphic bundle over the Riemann surface, joint with an auxiliar vector field, so-called Higgs field. This theory started around thirty years ago, with Hitchin’s work, when he reduced the self-duality equations from dimension four to dimension two, and so, studied those equations over Riemann surfaces. Hitchin baptized those fields as Higgs fields because in the context of physics and gauge theory, they describe similar particles to those described by the Higgs bosson. Later, Simpson used the name Higgs bundle for a holomorphic bundle together with a Higgs field. Today, Higgs bundles are the subject of research in several areas such as non-abelian Hodge theory, Langlands, mirror symmetry, integrable systems, quantum field theory (QFT), among others. The main purposes here are to introduce these objects, and to present a brief but complete construction of the moduli space of Higgs bundles.
Country:Kérwá
Institution:Universidad de Costa Rica
Repositorio:Kérwá
OAI Identifier:oai:kerwa.ucr.ac.cr:10669/81814
Online Access:https://revistas.ucr.ac.cr/index.php/matematica/article/view/38315
https://hdl.handle.net/10669/81814
Keyword:Higgs bundles
Hodge bundles
Moduli spaces
Stable triples
Vector bundles
Fibrados de Higgs
Fibrados de Hodge
Espacios móduli
Triples estables
Fibrados vectoriales