On KKLT/CFT and LVS/CFT dualities

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 (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 h1,1 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 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

The Swampland: Introduction and Review

“…For example, the CFT duals to the type IIA vacua of [] were studied in []. For the KKLT setup, work on the CFT duals was done in [], and for the LVS scenario the CFT duals were studied in [] (see also [] for general studies). In all situations, there were no explicit constructions of the CFTs, but rather only certain properties of them were deduced.…”

What if string theory has no de Sitter vacua?

“…Perhaps the most interesting way to check the consistency of an AdS landscape would be to first prove the existence of a CFT landscape with the right properties such that the CFT's are candidate duals to AdS vacua with scale separation [178,179]. This is an open avenue for research, and given the recent progress in understanding the spaces of consistent CFT's one can be hopeful.…”

Swampland variations on a theme by KKLT

“…where c is an order one coefficient and m is the lightest non-vanishing (moduli) mass. For supersymmetric AdS 4 vacua, there would be a holographic dual conjecture for three-dimensional conformal field theories [46]. There is support for these conjectures at string tree level, though employing also more involved quantum aspects of string theory, like α , string-loop or even non-perturbative corrections, there are claims that both conjectures can be falsified.…”