Swampland conditions for higher derivative couplings from CFT

Abstract

There are effective field theories that cannot be embedded in any UV complete theory. We consider scalar effective field theories, with and without dynamical gravity, in D-dimensional anti-de Sitter (AdS) spacetime with large radius and derive precise bounds (analytically) on the coupling constants of higher derivative interactions ϕ2□kϕ2 by only requiring that the dual CFT obeys the standard conformal bootstrap axioms. In particular, we show that all such coupling constants, for even k ≥ 2, must satisfy positivity, monotonicity, and log-convexity conditions in the absence of dynamical gravity. Inclusion of gravity only affects constraints involving the ϕ2□2ϕ2 interaction which now can have a negative coupling constant. Our CFT setup is a Lorentzian four-point correlator in the Regge limit. We also utilize this setup to derive constraints on effective field theories of multiple scalars. We argue that similar analysis should impose nontrivial constraints on the graviton four-point scattering amplitude in AdS.

Into the EFThedron and UV constraints from IR consistency

“…Similarly it would be interesting to investigate the connections between the EFTs as those coming from the flat space limit of AdS/CFT, where the AdS EFT is constrained by the boundary CFT. For recent results see [33].…”

Exploring The Holographic Swampland

“…In a different context, similar results concerning the negativity of the γ(0, 2) anomalous dimension were also proven in [36]. More recently, such convexity relations have also been generalized to treat the OPE of two non-identical scalar primaries [37] and other closely related bounds for EFTs on AdS (which include the effect of dynamical gravity) have been obtained in [20,38]. These results served as a partial motivation in our previous paper [9] to conjecture that a similar negativity property for anomalous dimensions would correlate with Swampland conditions on AdS, supported from a number of examples in 4d string compactifications.…”

“…In an ideal world, this may provide a hope of understanding swampland constraints in terms of allowed behaviour within CFTs [8,9]. While CFT approaches to the swampland have already attracted a significant degree of attention in the literature [10][11][12][13][14][15][16][17][18][19][20][21][22], not much work has been carried out in the context of specific realisations. There was some discussion in older literature about properties of duals to explicit moduli stabilisation constructions [23][24][25], but the description is very complex and many details still remain to be worked out.…”

Mixed correlator dispersive CFT sum rules

“…The success of the modern conformal bootstrap stands upon the pillars of high precision numerical methods [1,2], and deeper understanding of the analytic structure of the bootstrap equations (see [3,4] and references therein). Numerical methods have led to high precision measurements of critical exponents of conformal field theories (CFTs) such as the 3D Ising [5][6][7][8] and the O(N ) models [9][10][11], while analytical methods have proven essential to the study of quantum gravity in Anti-de Sitter (AdS) spacetime [12][13][14][15][16][17][18] and perturbative CFTs [19,20]. In recent years, with the introduction of analytic functionals [21][22][23][24][25][26][27][28] and dispersion relation methods [29][30][31][32][33][34][35], the gap between numerics and analytics has greatly narrowed revealing new horizons for the bootstrap program.…”