Wormholes in the axiverse, and the species scale

Abstract

We analyze a large class of four-dimensional $\mathcal{N}=1$ low-energy realizations of the axiverse satisfying various quantum gravity constraints. We propose a novel upper bound on the ultimate UV cutoff of the effective theory, namely the species scale, which only depends on data available at the two-derivative level. Its dependence on the moduli fields and the number $N$ of axions matches expectations from other independent considerations. After an assessment of the regime of validity of the effective field theory, we investigate the non-perturbative gravitational effects therein. We identify a set of axionic charges supported by extremal and non-extremal wormhole configurations. We present a universal class of analytic wormhole solutions, explore their deformations, and analyze the relation between wormhole energy scales and species scale. The connection between these wormholes and a special subclass of BPS fundamental instantons is discussed, and an argument in favor of the genericity of certain axion-dependent effective superpotentials is provided. We find a lower bound increasing with $N\gg 1$ on the Gauss-Bonnet coefficient, resulting in an exponential suppression of non-extremal wormhole effects. Our claims are illustrated and tested in concrete string theory models.