Harmonic analysis of Narain partition function

In this post we visit this two papers: Harmonic analysis of 2d CFT partition functions and Scalar modular boostrap and zeros of the Riemann zeta function. There is a whole wealth of literature on this subject, mostly in the view of quantum gravity and ensemble averaging. We will get to discuss some of this today, from a more mathematical perspective. I am not sure how much physics we will get to.

Partition function of Narain CFTs

First let us review the partition function of Narain CFTs. Fix a positive number \(c\), which will be the central charge. A central charge \(c\) Narain CFT is given by a polarization of \(\Lambda^{c|c}\) FINISH THIS!!!

References:

• https://arxiv.org/pdf/2107.10744. The first paper about harmonic decomposition of Narain CFTs.
• https://arxiv.org/pdf/2208.02259. Discuss the relation between the scalar partition function and zeroes of the zeta function.
• https://arxiv.org/abs/2006.04855. The Maloney-Witten paper that discusses how Narain partition function average to 3D Chern-Simons theories, using the Siegel-Weil formula.