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The moduli space of two U(1) instantons on noncommutative $R^4$ and $R^3\times S^1$

Kimyeong Lee·David Tong·Sangheon Yi
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Abstract

We employ the ADHM method to derive the moduli space of two instantons in U(1) gauge theory on a noncommutative space. We show by an explicit hyperKähler quotient construction that the relative metric of the moduli space of two instantons on $R^4$ is the Eguchi-Hanson metric and find a unique threshold bound state. For two instantons on $R^3\times S^1$, otherwise known as calorons, we give the asymptotic metric and conjecture a completion. We further discuss the relationship of caloron moduli spaces of A, D and E groups to the Coulomb branches of three dimensional gauge theory. In particular, we show that the Coulomb branch of SU(2) gauge group with a single massive adjoint hypermultiplet coincides with the above two caloron moduli space.

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Kimyeong Lee, David Tong, Sangheon Yi. 2000-09-16. The moduli space of two U(1) instantons on noncommutative $R^4$ and $R^3\times S^1$. https://doi.org/10.1103/physrevd.63.065017

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