The EFT stringy viewpoint on large distances

TL;DR

This paper links EFT strings to infinite distance limits in 4d $ =1$ theories, showing that these strings become tensionless at the limits and provide bounds on the field range, supporting the Swampland Distance Conjecture.

Contribution

It proposes that all infinite distance limits in 4d $ =1$ EFTs can be described by EFT string flows, offering a bottom-up perspective on the Swampland Distance Conjecture.

Findings

EFT strings become tensionless at infinite distance limits.

The mass of the lightest tower scales as $m^2 \\sim \\mathcal{T}^w$, with $w=1,2,3$.

The results hold even with a non-trivial potential below the cut-off.

Abstract

We observe a direct relation between the existence of fundamental axionic strings, dubbed EFT strings, and infinite distance limits in 4d $\mathcal{N}=1$ EFTs coupled to gravity. The backreaction of EFT strings can be interpreted as RG flow of their couplings, and allows one to probe different regimes within the field space of the theory. We propose that any 4d EFT infinite distance limit can be realised as an EFT string flow. We show that along such limits the EFT string becomes asymptotically tensionless, and so the EFT eventually breaks down. This provides an upper bound for the maximal field range of an EFT with a finite cut-off, and reproduces the Swampland Distance Conjecture from a bottom-up perspective. Even if there are typically other towers of particles becoming light, we propose that the mass of the leading tower scales as $m^2\sim \mathcal{T}^w$ in Planck units, with $\mathcal{T}$ the EFT string tension and $w$ a positive integer. Our results hold even in the presence of a non-trivial potential, as long as its energy scale remains well below the cut-off. We check both proposals for large classes of 4d $\mathcal{N}=1$ string compactifications, finding that only the values $w=1,2,3$ are realised.