# Flux compactifications and the scalar potential

Does the scalar potential:

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

where $K$ is the Kähler potential and $W$ the superpotential, $D=\partial_I+\partial_IK$ and $I$ runs over all the moduli, 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. 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?

• Please always define your notation. I can guess what those objects are, but it is much better if your question briefly says what all those variables are supposed to be. – ACuriousMind Dec 2 '16 at 14:02
• There is an answer at physicsoverflow.org/37909 – Arnold Neumaier Dec 4 '16 at 17:25