determined after this field redefinition, $\hat{\psi}=N\psi $.

To obtain canonical kinetic terms we have to redefine the fields to go to the canonical basis by the inverse of the square root of the Kähler metric $K$ given by $$\hat{\psi}^{\dagger }K\hat{\psi}=(N\psi )^{\dagger }(N^{-1})^{\dagger
}N^{-1}N\psi  \label{kahlerdec}$$Thus $K=(N^{-1})^{\dagger }N^{-1}$ and hence $N=K^{-1/2}$, as claimed above. Using Supergravity (SUGRA) equations, the Kähler metric is obtained as $K_{\bar{a}b}=\partial ^{2}G/(\partial \Phi _{a}^{\dagger }\partial \Phi
^{b}) $ with $G$ the Kähler function and it determines both the Kinetic terms and the non-canonically normalised soft scalar mass squared matrices $\hat{m}_{\bar{a}b}^{2}$. In SUGRA, where $K_{\bar{a}b}$ represents a metric, $N^{-1} $ is also a Hermitian matrix, such that $N^{-1}=(N^{-1})^{\dagger }$ and hence it can be conventionally written as [@dreiner; @peddie] $$K=(N^{-1})^{\dagger }N^{-1}=V^{\dagger }X^{2}V\Leftrightarrow
N^{-1}=V^{\dagger }XV$$with V a unitary matrix diagonalising the Hermitian matrix $K$ and $X$ the square root of the eigenvalues of $K$. We call this solution the standard form of $N^{-1}$. Note that if $N^{-1}$ is a solution of Eq. (\[kahlerdec\]) then also $R.N^{-1}$ is a solution of Eq. (\[kahlerdec\]), with $R$ a unitary matrix. Of course physical quantities will not depend on $R$ and for any choice we must always obtain the same physical result. This is 