Fine Tuning, Sequestering, and the Swampland

TL;DR

The paper addresses whether EFTs coupled to gravity admit only finitely many tunings, and how this constrains IR CFTs within the swampland framework. It argues for finiteness from the Planck-scale structure of $L_{\text{eff}}$ and the finite string vacua, and analyzes CFT-to-gravity coupling across dimensions and SUSYs with explicit bounds. Key results include bounds such as $\text{rank}(\mathfrak{g}_{\text{tot}}) \leq 21$ in 6D $(2,0)$ theories and $r \leq 22$ for 4D ${\cal N}=4$ sectors, with ${\cal N}=2$ SCFTs from Calabi–Yau compactifications forming a finite set; cross-sector mixing is generic and cannot be fully sequestered, though some irrelevant deformations can be tuned away. The work narrows the swampland to a computable finite catalog and has implications for beyond-Standard-Model model-building, linking quantum gravity finiteness to IR dynamics and cosmology.

Abstract

We conjecture and present evidence that any effective field theory coupled to gravity in flat space admits at most a finite number of fine tunings, depending on the amount of supersymmetry and spacetime dimension. In particular, this means that there are infinitely many non-trivial correlations between the allowed deformations of a given effective field theory in the gravitational context. Fine tuning of parameters allows us to obtain some consistent CFTs in the IR limit of gravitational theories. Related to finiteness of fine tunings, we conjecture that except for a finite number of CFTs, the rest cannot be consistently coupled to gravity and belong to the swampland. Moreover, we argue that even though matter sectors coupled to gravity may sometimes be partially sequestered, there is an irreducible level of mixing between them, correlating and coupling infinitely many operators between these sectors.