Smallest 3d hyperbolic manifolds via simple 3d theories

摘要

We provide strong pieces of evidence that the mathematics of thethree-dimensional hyperbolic manifolds of the first, second and third smallestvolume is captured by the physics of the three-dimensional theories composed ofa 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.