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October 2013 Moduli spaces of instantons on toric noncommutative manifolds
Simon Brain, Giovanni Landi, Walter D. van Suijlekom
Adv. Theor. Math. Phys. 17(5): 1129-1193 (October 2013).

Abstract

We study analytic aspects of $\mathrm{U}(n)$ gauge theory over a toric noncommutative manifold $M_\theta$. We analyse moduli spaces of solutions to the self-dual Yang-Mills equations on $\mathrm{U}(2)$ vector bundles over four-manifolds $M_\theta$, showing that each such moduli space is either empty or a smooth Hausdorff manifold whose dimension we explicitly compute. In the special case of the four-sphere $S^4_\theta$ we find that the moduli space of $\mathrm{U}(2)$ instantons with fixed second Chern number $k$ is a smooth manifold of dimension $8k - 3$.

Citation

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Simon Brain. Giovanni Landi. Walter D. van Suijlekom. "Moduli spaces of instantons on toric noncommutative manifolds." Adv. Theor. Math. Phys. 17 (5) 1129 - 1193, October 2013.

Information

Published: October 2013
First available in Project Euclid: 21 August 2014

zbMATH: 1307.81055
MathSciNet: MR3262521

Rights: Copyright © 2013 International Press of Boston

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Vol.17 • No. 5 • October 2013
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