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Similarly the constraint F$_{H}$$_{u}$ = 0, along with the contraction yields λ $^{ij}$( L$_{i}$H$_{u}$ )( L$_{j}$H$_{u}$ ) = 0. This implies that L$_{i}$H$_{u}$ = 0 for all i . Therefore the two monomials LH$_{u}$ and H$_{u}$H$_{d}$ can be lifted by d = 4 terms in the superpotential Eq. (128). 

The other renormalizable flat directions are LLe, uud, QdL, QQQL, QuQd, uude and QuLe, dddLL, uuuee, QuQue, QQQQu, uudQdQd , and ( QQQ )$_{4}$ LLLe . The unique flat di- rections involving ( Q, u, e ) is lifted by d = 9, ( L, d ) by d = 7, and ( L, d, e ) by d = 5. The flat directions involving ( L, e ) , ( u, d ) and ( L, d, e ) are all lifted by d = 6 terms in the su- perpotential, while the rest of the flat directions are lifted already by d = 4 superpotential terms [407]. 

Vacuum degeneracy will also be lifted by SUSY breaking soft terms. The full flat direction potential in the simplest case reads [325, 326] 

where the SUSY breaking mass m$_{0}$, A ∼ 100 − 1000 GeV. 

<img src='content_image/351206.jpg'>

While considering the dynamics of a flat direction, in a cosmological setting, the super- potential of Eq. (126) generates a vanishing A -term. This is due to the fact that φ being light during inflation, i.e. H$_{inf}$ ≫ m$_{0}$ , it obtains large VEV during inflation due to random walk. As a result ψ field gets a large mass induced by the VEV of φ , which drives ψ to roll down to its minimum in less than one Hubble time, i.e. 〈 ψ 〉 = 0. The A -term being proportional to ψ vanishes in this limit, and does not play any dynamical role during and after inflation. In other words, the ψ field being super massive decouple from the dynamics. 

The A -term in Eq. (129) violates the U (1) carried by the flat direction and thus provides the necessary source for B − L violation in AD baryogenesis. In general, the coupling λ is complex and has an associated phase θ$_{λ}$ . Writing φ = | φ | exp( iθ ), one obtains a potential proportional to cos( θ$_{λ}$ + nθ ) in the angular direction. This has n discrete minima for the phase of φ , at each of which U (1) is broken. 

A very generic one-loop quantum corrections result in a logarithmic running of the soft SUSY breaking parameters . The effective potential for the flat direction is then given by [91, 408, 409]: 

<img src='content_image/351211.jpg'>

