Are tiny gauge couplings out of the Swampland?

TL;DR

The paper shows that in AdS/CFT with an Einstein gravity dual, extremely weak bulk gauge couplings are incompatible with quantum gravity due to black hole thermodynamics, imposing $g^2$ not vanishing faster than $\sim \exp(\ell^{d-1}/G)$ as $G\to 0$, which implies the dual CFT current two-point function coefficient $C_J$ cannot grow faster than $\exp(N^2)$. It also derives a logarithmic relation between the EFT cutoff, Planck scale, and AdS radius, connecting bulk nonperturbative effects to boundary data. These results provide a concrete holographic Swampland constraint on how weak a gauged symmetry can be and sharpen our understanding of the interplay between bulk EFT validity and boundary operator data.

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.