I was reading this paper, and while I did, I have one question:

Why is that

In the supergravity literature, one often formulates local special geometry
in terms of a section of a different bundle. This section is denoted as $V$ and is
related to $v$ by

$$V \equiv e^{K/2}v$$,
where $K$ is Kaehler potential? That is, why is that it is no longer written as $V$ (aka the symplectic section), but now there is a factor of $e^{K/2}$ hanging around in front of $v$? Why this form?

Please note that

the geometries appearing in $N = 2$ supergravity theories are
denoted as local special geometries. In mathemetics literature the local special geometry is called ’projective special geometry’.

Extra notes in order to clarify any vague definitions above:

On p.15 it says

There exists a holomorphic $Sp(2n+ 2;\mathbf{R})$-vector bundle $\mathcal{H}$ over the manifold and a holomorphic section $v(z)$ of $\mathcal{L} \otimes \mathcal{H}$. Note that $\mathcal{L}$ denotes the holomorphic line bundle over the manifold, of which the first Chern class equals the cohomology class of the Kahler form.

This post imported from StackExchange Physics at 2015-12-24 12:30 (UTC), posted by SE-user PhilosophicalPhysics