A species or weak-gravity bound for large N gauge theories coupled to gravity

Abstract

Causality constrains the gravitational interactions of massive higher spin particles in both AdS and flat spacetime. We explore the extent to which these constraints apply to composite particles, explaining why they do not rule out macroscopic objects or hydrogen atoms. However, we find that they do apply to glueballs and mesons in confining large N gauge theories. Assuming such theories contain massive bound states of general spin, we find parametric bounds in (3 + 1) spacetime dimensions of the form N M P l Λ QCD relating N , the QCD scale, and the Planck scale. We also argue that a stronger bound replacing Λ QCD with(2.10)After smearing, δF smeared is a function of ρ, various OPE coefficients, and polarization of the operator G J . It was argued in [3] that that the condition Im(δF smeared ) ≤ 0 for all polarizations of the operator G J cannot be satisfied in the limit ρ → 1 for J > 2.8where, J 0 = min(J, J − 2) , J 0 = min(J, J − 1) for m 1 = m 3 , J 0 = J 0 = J for m 1 = m 3 . (D.4)

Renormalization group flows, the a-theorem and conformal bootstrap

“…Of course, these AdS bounds imply analogous bounds for the flat space effective field theory if and only if the CFT description does not breakdown as we take the flat space limit. It is not alway obvious that a smooth flat space limit R AdS → ∞ exists for any AdS theory, for example see [43]. However, the fact that all interactions of the dilaton are non renormalizable ensures that a smooth flat space limit of the AdS theory (3.1) does exist.…”

A conjecture on the minimal size of bound states

“…Recently, constraints have been put forward on the existence of higher-spin, composite states of mass M and size R which appear point-like or elementary in the sense that R 1/M [56,57]. To make contact with our conjecture, which is specifically about non-elementary bound states, a generalization of the causality arguments of [56,57] would be needed. Note that our constraint is stronger as it excludes bound states of size R 1/m , with m the mass of the heaviest stable constituent particle.…”

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].…”

“…In particular, the coupling constant α 3 for the φ 3 interaction has positive mass dimension for D ≤ 5. So, this coupling can lead to large mixing effects in the dual CFT when we take the flat space limit R AdS → ∞ [68]. In particular, when…”

“…The first type of arguments, as explained in the introduction, lead to precise bounds, however, require some assumption about the Regge boundedness of the 4-point amplitude. Whereas, positivity of the eikonal phase-shift seems to be a more rigorous condition [101] 35 which leads to non-trivial constraints [39,67,68,101,[105][106][107][108][109][110], however, these constraints in some sense are parametric in nature. On the other hand, by now it is known that both types of bounds can be obtained in AdS from the same CFT sum-rule (3.11).…”