# Smallest 3d hyperbolic manifolds via simple 3d theories

## TL;DR

This paper suggests that the smallest 3D hyperbolic manifolds' complex mathematical structures can be understood through specific 3D physical theories involving complex bosons, Dirac fermions, and Chern-Simons gauge fields.

## Contribution

It provides evidence linking the geometry of smallest hyperbolic manifolds to particular 3D quantum field theories with specific matter content and Chern-Simons levels.

## Key findings

- Mathematical structures of smallest hyperbolic manifolds are captured by 3D theories.
- Specific gauge theories with complex bosons and fermions correspond to these manifolds.
- Evidence supports a deep connection between geometry and quantum field theory.

## Abstract

We provide strong pieces of evidence that the mathematics of the three-dimensional hyperbolic manifolds of the first, second and third smallest volume is captured by the physics of the three-dimensional theories composed of a complex boson and a Dirac fermion, both of unit charge, coupled to a U(1) gauge field with the Chern-Simons level $-5/2$, $-7/2$ and $-3/2$, respectively.