# Can an instanton in Weyl gauge be a Wilson loop?

+ 1 like - 0 dislike
44 views

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?

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\varnothing$ysicsOverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.