$G$ to be $$G = A^i\chi_i + A^0 (-3\Omega+\bar\Omega),$$ where the $A$’s are constants. As a result $G$ can have a component in the $(3,0)$ direction which is IASD, as opposed to the $(2,1)$ and $(0,3)$ components which are ISD. This violates the standard lore according to which supersymmetric three-form fluxes in Calabi-Yau compactifications of type IIB string theory are constrained to be $(2,1)$ and in particular ISD. Moreover, this renders the flux contribution to the tadpole non-positive definite. To see this we write the tadpole in the form $$\int H_{RR} \wedge H_{NS} =\ii\ee^{\phi} \int G\wedge \bar G.$$ Using that the metric on moduli space $g_{i \bar j}$ and the Kähler potential $K$ are represented by $$g_{i \bar j}=\ii e^K \int\chi_i \wedge\bar\chi_j  > 0 \qquad {\rm and } \qquad
\ii\int\bar\Omega\wedge\Omega = e^K> 0,$$ and are both positive definite we obtain a negative contribution to the tadpole from a particular component of $G$ namely $$i\int (-3\Omega + \bar\Omega) \wedge(-3\bar\Omega+\Omega) = - 8 e^K <
0.$$ Thus by turning on enough of this flux component we get an indefinite space of supersymmetric fluxes. This results in flux vacua with a finite tadpole in new directions of flux space. Some of these directions 