At tree level, the Kähler potential is given by (neglecting complex structure)

$K = -\ln(-\mathrm{i}(\tau - \bar{\tau})) - 2\ln(V_{CY})$

where $V_{CY} = \frac{1}{6} \kappa_{abc}t^at^bt^c$ ia the the two cycle volume.

In some literature this is written in form of Kähler moduli variables as $V_{CY}=-i(\rho_a - \bar{\rho_a})t^a $ where $\rho = b + i\tau$. $\tau$ here is 4 cycle modulus.

In some other literature this is given as $V_{CY}=-3i(\rho - \bar{\rho}) $ where $\rho = b + ie^{4u}$. $u$ fixes the volume of Calabi-Yau.

So my question is are these two equivalent? Would the $\rho\bar\rho$ component of the Kähler metric be the same?

This post imported from StackExchange Physics at 2015-04-25 19:21 (UTC), posted by SE-user sol0invictus