such a gauge group will induce a non-perturbative potential [899, 900]. Note that usually the K¨ ahler potential also obtains non-perturbative corrections [638–640], however, for a choice of W$_{0}$ it is possible to neglect them $^{109}$. With the help of the above superpotential and the K¨ ahler potential, the resulting minimum is found to be the SUSY one (for a pedagogical discussion, see [47]): where T$_{m}$ denotes the minimum. Note that the potential is adS in the minimum, and requires uplifting to get a dS universe. As suggested by KKLT, this can be achieved by adding SUSY breaking contributions, such as anti-D3 brane ( D 3), although breaks explicitly, its effect can be made small by the choice of brane tension, or in other words placing the D 3 brane in a warped geometry [55], whose contribution turns out to be: where C > 0, given in terms of the brane tension and the six dimensional volume. The addition of D 3 lifts the potential keeping the minimum almost intact, T ≃ T$_{m}$ , for which either the total potential vanishes or become dS. For | T | → ∞ , potential V → 0 leads to decompactification to 10 d . Thus, the potential is separated by the barrier which can keep the metastable minimum stable enough for the life time of the universe [55, 901]. Amongst various realizations of assisted inflation, N-flation is perhaps the most interesting one $^{110}$. The idea is to have N ∼ 300( M$_{P}$/f ) ∼ 10 4 number of axions, where f is the axion decay constant, of order f ∼ 0 . 1 $_{M}$− 1 P . These axions can drive inflation simultaneously with 3. N-flation V ¯ D 3 = C ( T + T ) $_{2}$, (472) D$_{T}$W ( T$_{m}$ ) = − aAe aT$_{m}$ − 3( W$_{0}$ + Ae − $^{aT$_{m}$}$) T + T$_{m}$ = 0 , (470) V ( T$_{m}$,T$_{m}$ ) = − 3( W$_{0}$ + Ae $^{T$_{m}$}$) 2 ( T$_{m}$ + T$_{m}$ ) 3 = − ( aAe − $^{aT$_{m}$}$) 2 3( T$_{m}$ + T$_{m}$ ) < 0 (471) 109 There are two kinds of string corrections, string loop corrections in powers of g$_{s}$ ∼ e φ and α ′ ∼ 1 /M 2 s type corrections. It is known that non-renormalization theorem forbids holomorphic superpotential to obtain corrections of either type [637]. However, the K¨ ahler potential is not similarly protected. 110 There are also realizations of assisted inflation via branes [558, 559] in a type IIB setting, with a large number of Kaluza Klein modes [285], exponential potentials arising from a generic string compactifica- tion [548], and in a M-theory setting with the help of large number of NS-5 branes in [560], etc. 227