Abstract
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 ( $$ \mathcal{N}=1 $$ for KKLT and $$ \mathcal{N}=0 $$ 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 h1,1 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 contribution to 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.
Highlights
Landscape have Conformal Field Theory (CFT) duals and if so what the properties of these theories are
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 compactifications
Besides a different amount of supersymmetry (N = 1 for KKLT and N = 0 for Large Volume Scenario (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 h1,1 Kahler moduli have this property
Summary
It is more illustrative to approach the AdS5 vacuum from the perspective of flux compactifications of type IIB string theory on S5, since that is the more natural way to compare this background with the KKLT and LVS ones One starts in this case from the Freund-Rubin ansatz in which the metric is maximally symmetric, G3 = 0, the axiodilaton S constant and (F5)mnpqr ∝ ǫmnpqr (with indices running along the compact dimensions; a similar expression holds for the non-compact dimensions from self-duality of F5). The effective cosmological constant of the non-compact 5D component of the spacetime is given by the value of the potential at the minimum (Λ = V |min) In this case, it is negative giving rise to AdS5 with AdS radius equal to the radius of the compact manifold, i.e. RAdS = RS5. All Kaluza-Klein (KK) modes have masses of order m ∼ 1/RAdS and there are many operators with conformal dimension of order O(1)
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