JournalsjncgVol. 7, No. 3pp. 677–708

Nonperturbative spectral action of round coset spaces of SU(2)

  • Kevin Teh

    Caltech, Pasadena, USA
Nonperturbative spectral action of round coset spaces of SU(2) cover
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Abstract

We compute the spectral action of SU(2)/Γ\Gamma with the trivial spin structure and the round metric and find it in each case to be equal to 1Γ(Λ3f^(2)(0)14Λf^(0))+O(Λ)\frac{1}{\vert \Gamma \vert}(\Lambda^3 \hat{f}^{(2)}(0) - \frac{1}{4}\Lambda \hat{f}(0) )+ O(\Lambda^{-\infty}). We do this by explicitly computing the spectrum of the Dirac operator for SU(2)/Γ\Gamma equipped with the trivial spin structure and a selection of metrics. Here Γ\Gamma is a finite subgroup of SU(2). In the case where Γ\Gamma is cyclic, or dicyclic, we consider the one-parameter family of Berger metrics, which includes the round metric, and when Γ\Gamma is the binary tetrahedral, binary octahedral or binary icosahedral group, we only consider the case of the round metric.

Cite this article

Kevin Teh, Nonperturbative spectral action of round coset spaces of SU(2). J. Noncommut. Geom. 7 (2013), no. 3, pp. 677–708

DOI 10.4171/JNCG/131