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File:Taub–NUT instanton bow diagram.svg

Original file ‎(SVG file, nominally 171 × 92 pixels, file size: 14 KB)

Captions

Captions

bow diagram corresponding to an instanton on [[:wikipedia:Taub–NUT space]]

Summary

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Description
English: Bow diagram corresponding to the moduli space of a Yang–Mills instanton (anti-self-dual connection) on wikipedia:Taub–NUT space, following Sergey A. Cherkis, "Moduli Spaces onf Instantons on the Taub–NUT Space", arXiv:0805.1245, Figure 1 and ibid., "Instantons on Gravitons, arXiv:1007.0044, Figure 2. This gives a diagram encoding the realization of the moduli space of an instanton on Taub–NUT space via hyperkähler reduction from Nahm data. Here, l describes the size of the Taub–NUT circle fibre; λ describes eigenvalues of the asymptotic monodromy of the connection along the Taub–NUT circle fibre; and R₀, R₁, and R₂ are ranks of vector bundles living on each partition of the interval [-l/2, l/2], which determine the monopole and instanton numbers.
Date
Source Own work
Author Osteologia

LaTeX source code: 

\documentclass[tikz,crop,convert={outfile=\jobname.svg}]{standalone}
\usetikzlibrary{decorations.pathmorphing}
\begin{document}
\begin{tikzpicture}
\draw [
line join=round,
decorate, decoration={
    zigzag,
    segment length=4,
    amplitude=.9,post=lineto,
    post length=2pt
}]  (-2,0) -- (2,0);
\draw (-2,0) .. controls (-1,2) and (1,2) .. (2,0);
\filldraw [black] (-2,0) circle (2pt) node[anchor=north] {\(-l/2\)};
\filldraw [black] (2,0) circle (2pt) node[anchor=north] {\(l/2\)};
\filldraw [black] (-0.6,0) circle (2pt) node [anchor=north] {\(-\lambda/2\)};
\filldraw [black] (0.6,0) circle (2pt) node [anchor=north] {\(\lambda/2\)};
\draw (-1.3,0) node [anchor=south] { \(R_1\) };
\draw (0,0) node [anchor=south] { \(R_2\) };
\draw (1.3,0) node [anchor=south] { \(R_3\) };
\end{tikzpicture}
\end{document}

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w:en:Creative Commons
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Date/TimeThumbnailDimensionsUserComment
current15:39, 1 September 2019Thumbnail for version as of 15:39, 1 September 2019171 × 92 (14 KB)Osteologia (talk | contribs)User created page with UploadWizard

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