Universal Bounds on Charged States in 2d CFT and 3d Gravity

TL;DR

This paper establishes universal bounds on the lightest charged states in 2d CFTs with abelian symmetry and discusses implications for 3d gravity, providing explicit bounds and examples that saturate them.

Contribution

It derives explicit bounds on charged state dimensions in 2d CFTs with abelian symmetry and explores their implications for 3d gravitational theories.

Findings

Bound scales with central charge c

Examples saturate the bounds parametrically

Any such theory must contain a state with charge-to-mass ratio above a minimal lower bound

Abstract

We derive an explicit bound on the dimension of the lightest charged state in two dimensional conformal field theories with a global abelian symmetry. We find that the bound scales with $c$ and provide examples that parametrically saturate this bound. We also prove than any such theory must contain a state with charge-to-mass ratio above a minimal lower bound. We comment on the implications for charged states in three dimensional theories of gravity.