K j i = ( K − $^{1}$) j i = δ j $_{i}$) $^{32}$. The kinetic terms for the scalars take the form: The real part of the gauge kinetic function matrix is given by Re f$_{ab}$ . In the simplest case, it is just a constant, f$_{ab}$ = δ$_{ab}$/g 2 $_{a}$, and the kinetic terms for the gauge potentials, A a $_{µ}$, are given by $^{33}$: SUGRA will be broken if one or more of the F$_{i}$ obtain a VEV. The gravitino, spin ± 3 / 2 component of the graviton, then absorb the goldstino component to become massive. Re- quiring classically 〈 V 〉 = 0, as a constraint to obtain the zero cosmological constant, one obtains In case of SUGRA at tree-level with minimal kinetic term, the super-trace formula modifies to (for D -flat directions): where n$_{φ}$ is the number of the chiral multiplets in the spontaneously broken SUGRA. 1. SUSY generalization of one-loop effective potential with Λ$_{c}$ being a momentum cut-off and µ the scale parameter. The renormalized potential will not depend on Λ$_{c}$, and the dots stand for Λ$_{c}$-independent contributions. A SUSY generalization of one-loop effective potential, Eq. (98), is given by [412, 413]: 32 In general the superpotential can have non-renormalizable contributions. Similarly, the K¨ ahler potential can be expanded as: K = φ$_{i}$φ ∗ i + ( k ij φ$_{i}$φ$_{j}$φ ∗ k + c.c. ) /M$_{P}$ + ( k ij $_{kl}$φ$_{i}$ φ$_{j}$φ ∗ $^{k}$φ ∗ $^{l}$φ ∗ $^{k}$φ ∗ l + k ijk l φ$_{i}$φ$_{j}$φ$_{k}$φ ∗ l + c.c. ) /M 2 $_{P}$+ · · · ). We will discuss no-Scale SUGRA where the choice of K¨ ahler potential plays an important role in maintaining flat potential during inflation. 33 In general, f$_{ab}$ = δ$_{ab}$ (1 /g 2 a + f i $_{a}$φ$_{i}$ /M$_{P}$ + · · · ). The gauginos masses are typically given by m$_{λ}$ a = Re[ f i $_{a}$] 〈 F$_{i}$ 〉 / 2 M$_{P}$ . For a universal gaugino masses, f i a are the same for all the three gauge groups of MSSM. 62 ∂ $^{2}$K ∂φ$_{i}$∂φ ∗ j D$_{µ}$φ$_{i}$D µ $_{φ}$∗ j . (137) 1 4 (Re f$_{ab}$ ) F a $_{µν}$F µν a . (138) m 2 3 / 2 = 〈 K i $_{j}$F$_{i}$ F ∗ $^{j}$〉 3 M 2 P = $_{e}$〈 K 〉 /M 2 P |〈 W 〉| 2 M 4 P . (139) Str M 2 ≡ ∑ spin J ( − 1) 2 $^{J}$(2 J + 1) tr M 2 J ≈ 2( n$_{φ}$ − 1) m 2 3 / $_{2}$, (140) Δ V = 1 64 π $_{2}$Str ( M 0 ) Λ 4 c ln ( Λ 2 c µ 2 ) + 1 32 π $_{2}$Str ( M 2 ) Λ 2 c + 1 64 π $_{2}$Str ( M $^{4}$ln ( M 2 Λ 2 c )) + ... , (141)