Smallest 3d hyperbolic manifolds via simple 3d theories

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

Figure 1

The Whitehead link, from which three smallest hyperbolic manifolds can be obtained by the Dehn filling.