On KKLT/CFT and LVS/CFT Dualities

We present a general discussion of the properties of three dimensional CFT duals to the AdS string theory vacua coming from type IIB Calabi-Yau flux compactifi- cations. Both KKLT and Large Volume Scenario (LVS) minima are considered. In both cases we identify the large 'central charge', find a separation of scales between the radius of AdS and the size of the extra dimensions and show that the dual CFT has only a limited number of operators with small conformal dimension. Differences between the two sets of duals are identified. Besides a different amount of supersymmetry (N = 1 for KKLT and N = 0 for LVS) we find that the LVS CFT dual has only one scalar operator with O(1) conformal dimension, corresponding to the volume modulus, whereas in KKLT the whole set of h 1,1 Kahler moduli have this property. Also, the maximal number of degrees of freedom is estimated to be larger in LVS than in KKLT duals. In both cases we explic- itly compute the coefficient of the logarithmic contributionto the one-loop vacuum energy which should be invariant under duality and therefore provides a non-trivial prediction for the dual CFT. This coefficient takes a particularly simple form in the KKLT case.