where φ$_{i}$ are complex scalar fields and the phase χ is a real field constrained by where D$_{µ}$ is a gauge covariant derivative that reduces to the partial derivative when the gauge fields vanish, P$_{1}$ is the projection operator along Φ and P$_{2}$ along Ψ, where and the corresponding equation of motion where R = √$_{Φ}$$_{†}$$_{Φ. We are interested in the background dynamics where all the fields are}$ homogeneous in time, and for simplicity we study only the radial motion, such that Φ = R ˆ e$_{Φ}$ , where ˙ ˆ e$_{Φ}$ = 0 (the dot denotes derivative w.r.t time). Then the equation of motion simplifies to A notable feature is that the fields have non-minimal kinetic terms, since the field manifold defined by the flat direction is curved, actually a hyperbolic manifold. This results into the usual equation of motion for one scalar field with a potential for the radial mode except for the factor 1 / 2, which makes the potential effectively flatter in this direction. This can be traced to the square root nature of H$_{u}$ in Eq. (367). As far as our example of LH$_{u}$ is concerned there are only three families which we can account for. The flattest MSSM direction, QuQue , is lifted by n = 9 superpotential operator, QuQuQuH$_{d}$ee . The flat direction QuQue is an 18 complex dimensional manifold, Ref. [407]. The largest D-flat direction is only 37 complex dimensional [407]. One can imagine a larger representation which will have larger number of D -flat directions which 171 The field configuration in Eq. (367) leads to an effective Lagrangian for the flat direction fields φ$_{i}$ , ∂$_{µ}$χ = ∑ j J φ j 2 i k | φ$_{k}$ | 2 , J φ i = $_{φ}$∗ $_{i}$∂$_{µ}$ φ$_{i}$ − φ$_{i}$∂$_{µ}$$_{φ}$∗ i . (368) L = | D$_{µ}$H$_{u}$ | 2 + 3 ∑ i =1 | D$_{µ}$L$_{i}$ | 2 − V = 1 2 ∂$_{µ}$ $_{Φ}$† ( 1 + P$_{1}$ − 1 2 P$_{2}$ ) ∂ $^{µ}$Φ − V , (369) ¯ φ = ( φ$_{1}$ φ$_{2}$ φ$_{3}$ ) T , Φ =   ¯ φ ¯ φ ∗   , Ψ =   ¯ φ − ¯ φ ∗   , (370) ∂$_{µ}$∂ $^{µ}$Φ + 3 H ˙ Φ + ( 1 − 1 2 P$_{1}$ + P$_{2}$ ) ∂V ∂ Φ † − $_{R}$− 2 [ ∂$_{µ}$ $_{Ψ (Ψ}$†$_{∂}$ $^{µ}$Φ) + Ψ ( ∂$_{µ}$ $_{Ψ}$†$_{P}$$_{2}$$_{∂}$ $^{µ}$Φ) + 1 2 Φ ∂$_{µ}$ $_{Φ}$† ( 1 − P$_{1}$ − 3 2 P$_{2}$ ) ∂ $^{µ}$Φ ] = 0 , (371) ¨ R + 3 H ˙ R + 1 2 ∂V ∂R = 0 , (372)