Wormholes and spectral statistics in the Narain ensemble

We study the spectral statistics of primary operators in the recently formulated ensemble average of Narain's family of free boson conformal field theories, which provides an explicit (though exotic) example of an averaged holographic duality. In particular we study moments of the partition function by explicit computation of higher-degree Eisenstein series. This describes the analog of wormhole contributions coming from a sum of over geometries in the dual theory of U(1) gravity in AdS(3). We give an exact formula for the two-point correlation function of the density of primary states. We compute the spectral form factor and show that the wormhole sum reproduces precisely the late time plateau behaviour related to the discreteness of the spectrum. The spectral form factor does not exhibit a linear ramp.

Automated summary

This paper studies the spectral statistics of primary operators in the ensemble average of Narain's family of free boson conformal field theories, by computing higher-degree Eisenstein series. The results show that the spectral form factor does not exhibit a linear ramp.