Advances in Theoretical and Mathematical Physics

Volume 17 (2013)

Number 5

Moduli spaces of instantons on toric noncommutative manifolds

Pages: 1129 – 1193

DOI: http://dx.doi.org/10.4310/ATMP.2013.v17.n5.a5

Authors

Simon Brain (Unité de Recherche en Mathematiques, Université du Luxembourg (Campus Kirchberg), Luxembourg)

Giovanni Landi (Dipartimento di Matematica, Università di Trieste, Italy; INFN, Sezione di Trieste, Italy)

Walter D. van Suijlekom (Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen, The Netherlands)

Abstract

We study analytic aspects of $U(n)$ gauge theory over a toric noncommutative manifold Mθ. We analyse moduli spaces of solutions to the self-dual Yang-Mills equations on $U(2)$ 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 $U(2)$ instantons with fixed second Chern number $k$ is a smooth manifold of dimension $8k - 3$.

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