# Fine Tuning, Sequestering, and the Swampland

## TL;DR

This paper proposes that effective field theories coupled to gravity can only be finely tuned finitely many times, leading to a finite set of consistent theories, and suggests most non-supersymmetric CFTs belong to the swampland due to these constraints.

## Contribution

It introduces a conjecture that limits the number of fine tunings in gravitational EFTs and links this to the swampland, providing new insights into the structure of consistent theories.

## Key findings

- Finite number of fine tunings depending on supersymmetry and dimension
- Most CFTs cannot be coupled to gravity and are in the swampland
- Irreducible mixing persists between matter sectors coupled to gravity

## 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.