On KKLT/CFT and LVS/CFT Dualities

TL;DR

This paper explores the properties of three-dimensional conformal field theory (CFT) duals to type IIB string theory vacua from Calabi-Yau flux compactifications, comparing KKLT and LVS scenarios in terms of operator content, degrees of freedom, and vacuum energy contributions.

Contribution

It provides a detailed analysis of the dual CFT characteristics for KKLT and LVS vacua, highlighting differences in operator spectrum, degrees of freedom, and vacuum energy coefficients.

Findings

Large central charge identified in both duals.

LVS dual has only one scalar operator with O(1) dimension.

KKLT dual has multiple Kähler moduli with similar properties.

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 compactifications. 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 $\mathcal{O}(1)$ conformal dimension, corresponding to the volume modulus, whereas in KKLT the whole set of $h^{1,1}$ K\"ahler 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 explicitly 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.