Asymptotics of Higgs bundles in the Hitchin component

SL(∞,ℝ), Higgs Bundles and Quantization

Geometry and Physics: Volume II ◽

10.1093/oso/9780198802020.003.0016 ◽

2018 ◽

pp. 419-432

Author(s):

Olivier Biquard

Keyword(s):

Surface Groups ◽

Higgs Bundles ◽

Hitchin Component

Nigel Hitchin recently proposed a theory of SL(∞, R)-Higgs bundles which should parametrize a Hitchin component of representations of surface groups into SL(∞, R). This chapter discusses some properties and propose a formal approximation of SL(∞, R) representations by SL(n, R) representations in the large N limit, where n goes to infinity.

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REPRESENTATIONS OF SURFACE GROUPS IN THE PROJECTIVE GENERAL LINEAR GROUP

International Journal of Mathematics ◽

10.1142/s0129167x11006787 ◽

2011 ◽

Vol 22 (02) ◽

pp. 223-279 ◽

Cited By ~ 4

Author(s):

ANDRÉ GAMA OLIVEIRA

Keyword(s):

Moduli Space ◽

Riemann Surfaces ◽

Connected Components ◽

Higgs Bundles ◽

Semisimple Lie Group ◽

Projective Bundles ◽

Compact Riemann Surfaces ◽

Hitchin Component ◽

Projective General Linear Group ◽

Closed Oriented Surface

Given a closed, oriented surface X of genus g ≥ 2, and a semisimple Lie group G, let [Formula: see text] be the moduli space of reductive representations of π1X in G. We determine the number of connected components of [Formula: see text], for n ≥ 4 even. In order to have a first division of connected components, we first classify real projective bundles over such a surface. Then we achieve our goal, using holomorphic methods through the theory of Higgs bundles over compact Riemann surfaces. We also show that the complement of the Hitchin component in [Formula: see text] is homotopically equivalent to [Formula: see text].

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On the Voevodsky motive of the moduli space of Higgs bundles on a curve

Selecta Mathematica ◽

10.1007/s00029-020-00610-5 ◽

2021 ◽

Vol 27 (1) ◽

Author(s):

Victoria Hoskins ◽

Simon Pepin Lehalleur

Keyword(s):

Moduli Space ◽

Moduli Spaces ◽

Characteristic Zero ◽

Rational Point ◽

Triangulated Category ◽

Higgs Bundles ◽

Projective Curve ◽

Smooth Projective Curve ◽

De Rham

AbstractWe study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a rational point. We show this motive is contained in the thick tensor subcategory of Voevodsky’s triangulated category of motives with rational coefficients generated by the motive of C. Moreover, over a field of characteristic zero, we prove a motivic non-abelian Hodge correspondence: the integral motives of the Higgs and de Rham moduli spaces are isomorphic.

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Torelli theorem for the moduli space of symplectic parabolic Higgs bundles

Bulletin des Sciences Mathématiques ◽

10.1016/j.bulsci.2021.102978 ◽

2021 ◽

pp. 102978

Author(s):

Sumit Roy

Keyword(s):

Moduli Space ◽

Higgs Bundles ◽

Torelli Theorem

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Local G2-manifolds, Higgs bundles and a colored quantum mechanics

Journal of High Energy Physics ◽

10.1007/jhep05(2021)002 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Max Hübner

Keyword(s):

Quantum Mechanics ◽

Gauge Theories ◽

Supersymmetric Quantum Mechanics ◽

Higgs Bundle ◽

Higgs Bundles ◽

View Point ◽

Yang Mills ◽

G2 Manifolds ◽

Supersymmetric Gauge ◽

M Theory

Abstract M-theory on local G2-manifolds engineers 4d minimally supersymmetric gauge theories. We consider ALE-fibered G2-manifolds and study the 4d physics from the view point of a partially twisted 7d supersymmetric Yang-Mills theory and its Higgs bundle. Euclidean M2-brane instantons descend to non-perturbative effects of the 7d supersymmetric Yang-Mills theory, which are found to be in one to one correspondence with the instantons of a colored supersymmetric quantum mechanics. We compute the contributions of M2-brane instantons to the 4d superpotential in the effective 7d description via localization in the colored quantum mechanics. Further we consider non-split Higgs bundles and analyze their 4d spectrum.

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