# Asymptotic behaviour and the moduli space of doubly-periodic instantons

Olivier Biquard; Marcos Jardim

Journal of the European Mathematical Society (2001)

- Volume: 003, Issue: 4, page 335-375
- ISSN: 1435-9855

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topBiquard, Olivier, and Jardim, Marcos. "Asymptotic behaviour and the moduli space of doubly-periodic instantons." Journal of the European Mathematical Society 003.4 (2001): 335-375. <http://eudml.org/doc/277473>.

@article{Biquard2001,

abstract = {We study doubly-periodic instantons, i.e. instantons on the product of a 1-dimensional complex torus $T$ with a complex line $\mathbb \{C\}$, with quadratic curvature decay. We determine the asymptotic behaviour of these instantons, constructing new asymptotic invariants. We show that the underlying holomorphic bundle extends to $T\times \mathbb \{P\}^1$. The converse statement is also true, namely a holomorphic bundle on $T\times \mathbb \{P\}^1$ which is flat on the torus at infinity, and satisfies a stability condition, comes from a doubly-periodic instanton. Finally, we study the hyperkähler geometry of the moduli space of doubly-periodic instantons, and prove that the Nahm transform previously defined by the second author is a hyperkähler
isometry with the moduli space of certain meromorphic Higgs bundles on the dual torus.},

author = {Biquard, Olivier, Jardim, Marcos},

journal = {Journal of the European Mathematical Society},

keywords = {Yang-Mills theory; instantons; gauge theory; moduli spaces; Higgs bundles; Nahm transform; holomorphic vector bundles; hyper-Kähler geometry; Yang-Mills theory; instantons; gauge theory; moduli spaces; Higgs bundles; Nahm transform; holomorphic vector bundles; hyper-Kähler geometry},

language = {eng},

number = {4},

pages = {335-375},

publisher = {European Mathematical Society Publishing House},

title = {Asymptotic behaviour and the moduli space of doubly-periodic instantons},

url = {http://eudml.org/doc/277473},

volume = {003},

year = {2001},

}

TY - JOUR

AU - Biquard, Olivier

AU - Jardim, Marcos

TI - Asymptotic behaviour and the moduli space of doubly-periodic instantons

JO - Journal of the European Mathematical Society

PY - 2001

PB - European Mathematical Society Publishing House

VL - 003

IS - 4

SP - 335

EP - 375

AB - We study doubly-periodic instantons, i.e. instantons on the product of a 1-dimensional complex torus $T$ with a complex line $\mathbb {C}$, with quadratic curvature decay. We determine the asymptotic behaviour of these instantons, constructing new asymptotic invariants. We show that the underlying holomorphic bundle extends to $T\times \mathbb {P}^1$. The converse statement is also true, namely a holomorphic bundle on $T\times \mathbb {P}^1$ which is flat on the torus at infinity, and satisfies a stability condition, comes from a doubly-periodic instanton. Finally, we study the hyperkähler geometry of the moduli space of doubly-periodic instantons, and prove that the Nahm transform previously defined by the second author is a hyperkähler
isometry with the moduli space of certain meromorphic Higgs bundles on the dual torus.

LA - eng

KW - Yang-Mills theory; instantons; gauge theory; moduli spaces; Higgs bundles; Nahm transform; holomorphic vector bundles; hyper-Kähler geometry; Yang-Mills theory; instantons; gauge theory; moduli spaces; Higgs bundles; Nahm transform; holomorphic vector bundles; hyper-Kähler geometry

UR - http://eudml.org/doc/277473

ER -

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