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Instantons are characterized by the winding number and a set of collective parameters (e.g. location of the centers of the instantons, their sizes and the inequivalent orientations in the global group space / space-time). Quantum fluctuations of a unit winding number instanton can either leave the collective parameters unchanged (non-zero modes), or change ...

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The ambiguity that people normally refer to is due to the lack of Borel summability of the perturbation series. Consider a series of the form $$A(g) = \sum_{n=1}^{\infty}{(-1)^n g^n (n!)}$$ If the coefficients $b_n$ are of order $1$, this series is obviously divergent. But we can compute its Borel sum. First compute the Borel transform: ...

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Maybe this would be better as a comment, since it is not a full answer, but I don't have enough reputation for that. The most important ambiguity is that there is an infinite number of functions that have the same asymptotic expansion. As an example, if $f(g)$ has some asymptotic expansion in $g$ as $g \to 0$ than $f(g) + e^{-1/g^2}$ has exactly the same ...

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I know this is a year old question, but I am going to attempt an answer. As far as I can tell, this is not really a caveat. The reason for this is that I can always set the overall phase of the quark mass determinant to be zero with a chiral U(1) transformation. For a discussion of this see for example the chapter on theta vacua in Weinberg's QFT book. The ...

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