Moduli Spaces of Instantons on Toric Noncommutative Manifolds

2012/04/10 by Brain, Simon, Landi, Giovanni, van Suijlekom, Walter D.
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1204.2148

Abstract

We study analytic aspects of U(n) gauge theory over a toric noncommutative manifold M_θ. We analyse moduli spaces of solutions to the self-dual Yang-Mills equations on U(2) vector bundles over four-manifolds M_θ, 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 S⁴_θ we find that the moduli space of U(2) instantons with fixed second Chern number k is a smooth manifold of dimension 8k-3.

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