scholarly journals The Limit of the Yang–Mills–Higgs Flow on Higgs Bundles

2016 ◽  
Vol 2017 (1) ◽  
pp. 232-276 ◽  
Author(s):  
Jiayu Li ◽  
Xi Zhang
Keyword(s):  
Higgs Bundles ◽  
Yang Mills

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

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.

scholarly journals Approximate Yang-Mills-Higgs metrics on flat Higgs bundles over an affine manifold

2014 ◽  
Vol 22 (4) ◽  
pp. 737-754
Author(s):  
Indranil Biswas ◽  
John Loftin ◽  
Matthias Stemmler
Keyword(s):  
Higgs Bundles ◽  
Affine Manifold ◽  
Yang Mills

The Narasimhan—Seshadri theorem for parabolic bundles: an orbifold approach

1995 ◽  
Vol 353 (1702) ◽  
pp. 137-171 ◽  
Keyword(s):  
Riemann Surface ◽  
Marked Point ◽  
Weak Compactness ◽  
Analogous Problem ◽  
Rational Approximations ◽  
Higgs Bundles ◽  
Equivalent Problem ◽  
Parabolic Bundle ◽  
Yang Mills ◽  
Parabolic Bundles

Given a stable parabolic bundle over a Riemann surface, we study the problem of finding a compatible Yang-Mills connexion. When the parabolic weights are rational there is an equivalent problem on an orbifold bundle. When the weights are irrational our method is to choose a sequence of approximating rational weights, obtain a corresponding sequence of Yang-Mills connexions on the resulting orbifold bundles and obtain the solution as the limit of this sequence: we need to consider mildly singular connexions which locally about a marked point take the form d — Aid# + a . Here A is a constant diagonal matrix whose entries depend on the weights and their rational approximations, 0 = arg(z) for z a local uniformizing (orbifold) coordinate centred on the marked point and a is an L 2 1 connexion matrix. In this context we find all the necessary gauge-theoretic tools to prove the theorem, including a version of Uhlenbeck’s weak compactness theorem, provided | A| is sufficiently small. (One of the advantages of this approach is that we do analysis on a compact orbifold rather than on the punctured surface.) Our methods also allow us to consider the analogous problem for stable parabolic Higgs bundles.

scholarly journals On a functional of Kobayashi for Higgs bundles

2020 ◽  
Vol 17 (13) ◽  
pp. 2050200
Author(s):  
Sergio A. H. Cardona ◽  
Claudio Meneses
Keyword(s):  
Mean Curvature ◽  
Vector Bundles ◽  
Kähler Manifold ◽  
Higgs Bundle ◽  
Inner Product ◽  
Higgs Bundles ◽  
Hermitian Metrics ◽  
Yang Mills ◽  
Holomorphic Vector Bundles ◽  
Kahler Manifold

We define a functional [Formula: see text] for the space of Hermitian metrics on an arbitrary Higgs bundle over a compact Kähler manifold, as a natural generalization of the mean curvature energy functional of Kobayashi for holomorphic vector bundles, and study some of its basic properties. We show that [Formula: see text] is bounded from below by a nonnegative constant depending on invariants of the Higgs bundle and the Kähler manifold, and that when achieved, its absolute minima are Hermite–Yang–Mills metrics. We derive a formula relating [Formula: see text] and another functional [Formula: see text], closely related to the Yang–Mills–Higgs functional, which can be thought of as an extension of a formula of Kobayashi for holomorphic vector bundles to the Higgs bundles setting. Finally, using 1-parameter families in the space of Hermitian metrics on a Higgs bundle, we compute the first variation of [Formula: see text], which is expressed as a certain [Formula: see text]-Hermitian inner product. It follows that a Hermitian metric on a Higgs bundle is a critical point of [Formula: see text] if and only if the corresponding Hitchin–Simpson mean curvature is parallel with respect to the Hitchin–Simpson connection.

Approximate Hitchin–Kobayashi correspondence for Higgs G-bundles

2014 ◽  
Vol 11 (07) ◽  
pp. 1460015 ◽  
Author(s):  
Ugo Bruzzo ◽  
Beatriz Graña Otero
Keyword(s):  
Reductive Group ◽  
Kähler Manifold ◽  
Higgs Bundle ◽  
Structure Group ◽  
Higgs Bundles ◽  
Yang Mills ◽  
Kahler Manifold ◽  
Group A ◽  
Compact Kähler Manifold

We announce a result about the extension of the Hitchin–Kobayashi correspondence to principal Higgs bundles. A principal Higgs bundle on a compact Kähler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian–Yang–Mills structure.

scholarly journals On 2k-Hitchin’s equations and Higgs bundles: A survey

2021 ◽  
pp. 2130003
Author(s):  
S. A. H. Cardona ◽  
H. García-Compeán ◽  
A. Martínez-Merino
Keyword(s):  
Vector Bundles ◽  
Complex Geometry ◽  
Higgs Bundles ◽  
Yang Mills ◽  
Basic Properties ◽  
Holomorphic Vector Bundles

We study the [Formula: see text]-Hitchin’s equations introduced by Ward from the geometric viewpoint of Higgs bundles. After an introduction on Higgs bundles and [Formula: see text]-Hitchin’s equations, we review some elementary facts on complex geometry and Yang–Mills theory. Then, we study some properties of holomorphic vector bundles and Higgs bundles and we review the Hermite–Yang–Mills equations together with two functionals related to such equations. Using some geometric tools we show that, as far as Higgs bundles are concerned, [Formula: see text]-Hitchin’s equations are reduced to a set of two equations. Finally, we introduce a functional closely related to [Formula: see text]-Hitchin’s equations and we study some of its basic properties.

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