form [325, 326, 416, 417] K = ∫ d $^{4}$θ 1 M 2 P ( $_{I}$†$_{I}$$_{)(}$$_{φ}$ †$_{φ}$$_{)}$$_{,}$ (142) where I is the inflaton whose energy density ρ ≈ 〈 ∫ d $^{4}$θI † I 〉 dominates during inflation, and φ is the flat direction. The interaction, Eq. (142), will generate an effective mass term in the Lagrangian in the global SUSY limit, given by L = ρ$_{I}$ M 2 P $_{φ}$†$_{φ}$ = 3 H 2 $_{$_{I}$φ}$†$_{φ ,}$ (143) m 2 φ = ( 2 + F ∗ I F$_{I}$ V ( I ) ) H $^{2}$. (144) where H$_{I}$ is the Hubble parameter during inflation. For a minimal choice of flat direction K¨ ahler potential K ( φ † , φ ) = φ † φ , during inflation the effective mass for the flat direction is found to be [325, 326] $^{36}$: Here it has been assumed that the main contribution to the inflaton potential comes from the F -term. If there were D -term contributions V$_{D}$ ( I ) to the inflationary potential, then a correction of order V$_{F}$ ( I ) / ( V$_{F}$ ( I ) + V$_{D}$ ( I )) must be taken into account. In purely D -term inflation there is no Hubble induced mass correction to the flat direction during inflation because F$_{I}$ = 0. However, when D -term inflation ends, the energy density stored in the D -term is converted to an F -term and to kinetic energy of the inflaton. Thus again a mass term m 2 φ = ±O (1) H 2 appears naturally, however the overall sign is undetermined [418]. There exists a choice of K¨ ahler potential for which there is no Hubble induced correction to the mass of the lights scalars. An example of this is provided by no-scale models, for which K ∼ ln( z + z ∗ + $_{φ}$† $_{i}$φ ), where z belongs to SUSY breaking sector, and φ$_{i}$ belongs to the matter sector, and both are measured in terms of reduced Planck mass [419–421] (for a review, see [422]). In no-scale models there exists an enhanced symmetry known as the Heisenberg symmetry [423], which is defined on the chiral fields as δz = ϵ ∗ φ $^{i}$, δφ i = ϵ $^{i}$, and δy i = 0, where y i are the hidden sector fields, such that the combinations η = z + z ∗ − φ ∗ $_{i}$φ$^{i}$, 3. No-scale SUGRA 36 If the K¨ ahler potential has a shift symmetry, or its of type no-scale model, the Hubble induced mass correction to the flat direction does not arise at the tree-level potential. 64