Are tiny gauge couplings out of the Swampland?

TL;DR

This paper demonstrates that extremely weak gauge couplings in Einsteinian quantum gravity on AdS are inconsistent with black hole thermodynamics and are thus in the Swampland, imposing bounds on dual CFT correlators.

Contribution

It establishes a lower bound on gauge couplings in AdS quantum gravity and relates it to constraints on dual CFT two-point functions, connecting Swampland criteria with holography.

Findings

Weak gauge couplings must not vanish faster than ^{ ext{exponential in } rac{ ext{AdS radius}^{d-1}}{G}}.

The dual CFT two-point function coefficient C_J cannot grow faster than ^{N^2}.

Reveals a logarithmic relation between the EFT cutoff, Planck mass, and AdS radius.

Abstract

There is significant evidence suggesting that continuous global symmetries are always gauged in quantum gravity. However, very weakly gauged symmetries seem global to an effective field theory expansion in powers of Newton's constant. We show that, at least for Einsteinian quantum gravity on AdS, such extremely weak gaugings are indeed in the Swampland: Consistency with AdS black hole thermodynamics requires the bulk gauge coupling $g^2$ not to vanish faster than $\sim\exp(\ell^{d-1}/G)$, where $\ell$ is the $AdS_{d+1}$ radius and $G$ is Newton's constant as we take the $G\rightarrow0$ limit. This translates to a constraint in the dual large $N$ CFT, namely, that the two-point function coefficient of the current $C_J$ cannot grow faster than $\exp(N^2)$ in the large $N$ limit. We also recover a previously known logarithmic relationship between the cutoff of the effective field theory in AdS, Planck's mass, and the AdS radius.