Does the scalar potential:

$$V=e^K(K^{I \bar{J}})D_IW D_{\bar{J}}\bar{W}-3|W|^2$$

arise **because** of the presence of fluxes?

If the fluxes are "turned off", does this mean $F_3=0$ and $H_3=0$, or that the integral of these field strengths over a particular cycle is zero (_i.e._ there are no non-trivial sources available in the theory)?

I usually see the $F_3$ and $H_3$ referred to as fluxes but I always thought these were field strengths.

To be specific this whole confusion arises from studying [*The Effective Action of $\mathcal{N}= 1$ Calabi-Yau orientifolds*][1]. Footnote $9$ says not having fluxes would result in not having the $V$ potential in the $4$D action; wouldn't also the kinetic terms for the field strength vanish?

[1]: https://arxiv.org/abs/hep-th/0403067