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  Can an instanton in Weyl gauge be a Wilson loop?

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I was wondering if one could write an $\mathrm{SU}(N)$-instanton as a Wilson loop. Since in temporal gauge, I can interpret a YM-instanton on $M\times\mathbb{R}$ as a one-parameter family of gauge connections on $M$. The instanton connects two Chern-Simons vacua at $x_0=\pm\infty$. If I compactify $x_0$ to a circle all the vacuum gauge fields are stacked on top of each other and an instanton should be nothing else than the transportation of the vacuum gauge field around a closed loop under the influence of an external force. The Wilson loop is $$W_\gamma=\mathrm{tr}\ \mathcal P\exp\oint_{S_1}{A(x_0)\ dx_0}$$ But how to build in the external force?

asked Jun 1, 2021 in Theoretical Physics by GaugeMe (10 points) [ revision history ]
recategorized Jun 9, 2021 by Dilaton

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