Moduli Stabilisation and the Holographic Swampland

Swampland conditions for higher derivative couplings from CFT

“…We will provide a partial answer to this question by leveraging the huge advancement in constraining the space of consistent CFTs from well-established conformal bootstrap axioms (for a review see [56]). The main logic of our argument parallels recent developments in constraining EFTs in AdS (with or without dynamical gravity) from rigorous analysis in the dual CFT [26,29,32,[57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74]. For example, the sign constraint on the φ 2 2 φ 2 coupling in the EFT (1.1) can be derived in AdS from the conformal bootstrap [58].…”

A CFT distance conjecture

“…Starting from a generic point of M, we can move to a nearby point by conformal perturbation theory. 17 For the distance to diverge, we need conformal perturbation theory to break down. This is indeed what happens at the free vector points: feynman perturbation theory applies, 18 but it is outside the standard framework of conformal perturbation theory, in that the perturbing operator (the supersymmetrization of A µ J µ ) is not part of the physical spectrum.…”

“…All known examples of N = 4 SCFTs are of course SYM theories, specified 16 The conclusion still holds if one allows for the requisite composite operator to be the product of an operator from the free hyper SCFT and an operator from the decoupled SCFT' -there is no candidate with the correct quantum numbers. 17 While not strictly needed for our considerations, a piece of lore which would be nice to establish more firmly is that conformal perturbation theory at an interior point of M has finite radius of convergence, see e.g. [109].…”

“…See[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] for some other works investigating the swampland conjectures using CFT techniques.…”

Tackling the SDC in AdS with CFTs

“…Proofs of no-go theorems applied to global symmetries as well as the Weak Gravity Conjectures in AdS were established by relating black hole quantities to conformal data [44][45][46]. More recently, positivity bounds were related to moduli stabilisation constraints in AdS 4 /CFT 3 , as well as possible connections to the SDC [47]. Closer to our setup, the classical moduli space has further been shown to be a coset in the case of AdS 5 gauged supergravity with sixteen (real) supercharges [48].…”