Chern-Simons Invariants from Ensemble Averages

Understand

We discuss ensemble averages of two-dimensional conformal field theories associated with an arbitrary indefinite lattice with integral quadratic form $Q$.

• We provide evidence that the holographic dual after the ensemble average is the three-dimensional Abelian Chern-Simons theory with kinetic term determined by $Q$.
• The resulting partition function can be written as a modular form, expressed as a sum over the partition functions of Chern-Simons theories on lens spaces.
• For odd lattices, the dual bulk theory is a spin Chern-Simons theory, and we identify several novel phenomena in this case.