Wormholes and Spectral Statistics in the Narain Ensemble

TL;DR

This paper investigates the spectral statistics of primary operators in the Narain ensemble, revealing how wormhole contributions influence spectral correlations and form factors in a holographic duality context.

Contribution

It provides explicit formulas for spectral correlations and analyzes wormhole effects in the Narain ensemble, advancing understanding of holographic dualities with free boson CFTs.

Findings

Wormhole contributions reproduce the late-time spectral plateau.

Spectral form factor lacks a linear ramp, indicating spectrum discreteness.

Exact formulas for two-point correlation functions of primary states.

Abstract

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.