Asymptotic behaviour and the moduli space of doubly-periodic instantons

Biquard, 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 -