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I started looking at Nekrasov's paper on instanton counting (https://arxiv.org/abs/hep-th/0206161), and I came across the term "framed G-instanton" right at the beginning on page 2.

What is a framed G-instanton?

Also, what are the physics and math prerequisites for understanding the instanton counting method? If anyone has any suggestions for reviews, I'all appreciate them as well.

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Let us consider some pure gauge theory on a 4-manifold $M$. A framed $G$-instanton refers to a pair $(A,p)$ where $A$ is an instanton in the principal $G$-bundle $P \to X$ and $p$ is a point in the fiber $P_x$ for a fixed $x\in X$. Then we consider the gauge transformations that stabilize $x$ but are non trivial at the fibers. I hope this helps a little bit.

Check page 6 of this PhD thesis

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  • $\begingroup$ Thanks @Marion! Is there any comment or implicit assumption in the definition about the boundary conditions on the gauge field or the gauge field strength at infinity? $\endgroup$
    – leastaction
    Commented Feb 15, 2017 at 0:43
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    $\begingroup$ Yes, the standard ones mainly the gauge field at infinity must be a pure gauge. Sheaf theoretically the restriction of the sheaf $E$ at $l_{\infty}$ must be isomorphic to $\oplus_n\mathcal{O}_X^n$ the trivial sheaf. $\endgroup$
    – Marion
    Commented Feb 15, 2017 at 0:45

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