This is in reference to the argument given towards the end of page $61$ of this review paper. There for the path-integral argument to work the author clearly needed some argument to be able to ignore the kinetic term(Kahler potential). But I can't get the argument fully.
Just above equation 5.5 in that review the author says, "..since the Kahler potential is irrelevant we may choose it at will,and in particular we may choose it very small. To a first approximation, in fact, we may ignore it..." And on Page 62 in his point 1, he says, "..Nothing in our argument assures that the resulting kinetic term in the Calabi-Yau sigma model will be sufficiently “large” to ensure that sigma model perturbation theory will be valid.."
- It would be great if someone can help make precise as to what the above argument means (..espeically the second part about "alrge"..) and flesh out its contents in may be an equation form or something..
Conceptually I would think that trying to ignore the kinetic term of the chiral fields is different than trying to ignore the kinetic term of the gauge fields. like say as written in equation 2.22 on page 11 of this paper.
- Now one can see that in the above paper (unlike in the initially linked review) the author is trying to ignore the gauge kinetic term by trying to take the gauge coupling $e \rightarrow \infty$ limit as in Page 30 of the above paper by Witten.
..but naively one might think that large gauge coupling is precisely the region where perturbative arguments would have started to fail and the entire idea of trying to minimize the classical potential would have started to become bad..
- But unlike in the review as linked to earlier, Witten's argument crucially needs the kinetic terms of the scalar chiral superfields (..from where the $F^2$ and the Yukawa terms come..). And Witten's argument also crucially needs the gauge kinetic term (from there the $D^2$ terms come..) Then why is he trying to justify the $e \mapsto \infty$ limit? Like he comments towards the end of Page 60, ``..the effects of finite e, are believed to be “irrelevant” in the technical sense of the renormalization group.."
It would be great if someone could explain these two arguments about ignoring the kinetic term of the gauge fields and the chiral fields.