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 φ 2 k φ 2 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 φ 2 2 φ 2 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.

Subleading Bounds on Chaos

“…general constraints. In section 5 we show that the chaos bounds obtained in this paper are completely consistent with CFT bounds of [17,18]. Finally, we conclude with some remarks in section 6.…”

“…As we mentioned before, CFT Regge correlators are a special case of the OTOC (1.1). These Regge correlators saturate the bound (1.8) in large-N CFTs that are dual to effective field theories in AdS with higher derivative four-point interactions [18,37,38]. We will discuss this in section 5.…”

“…It is well-known that certain CFT Regge correlators can be interpreted as a special case of the thermal OTOC (1.1) on Rindler space. 2 Recently, studies of these CFT Regge correlators have yielded an infinite set of constraints [17,18] beyond the MSS bound. So, it is a natural question to ask whether similar chaos bounds exist in general quantum systems with many degrees of freedom.…”

Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds

“…W (f ) p,q x p+q a q (6.6) 17 We have verified that this is indeed true for all the 4-graviton string amplitudes for details see B. 18 As for the photon case we could have considered 1]however this leads to a spectral coefficient ρ1 s1 2 + ρ 2 which doesn't seem to have a fixed sign from unitarity alone ρ 1 ≥ 0, ρ 1 ± ρ 2 ≥ 0. We shall use a different method to bound F h 1 (s 1 , s 2 , s 3 ).…”

“…In recent times, there has been an increase in interest in establishing two-sided bounds on ratios of parameters in front of higher dimensional operators in the EFT lagrangians. Recent work in this direction include [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Starting from the original attempts to constrain scalar EFTs, research has been extended to external particles carrying spin [7,21,22].…”