Adding flavor to the Narain ensemble

A bstract We revisit the proposal that ensemble average over free boson CFTs in two dimensions — parameterized by Narain’s moduli space is dual to an exotic theory of gravity three dubbed U(1) gravity. consider flavored partition functions, where usual genus g function weighted Wilson lines coupled conserved currents these theories. These functions obey a heat equation which relates deformations Riemann surface those chemical potentials measure charges. This allows us derive Siegel-Weil formula computes functions. The result takes form “sum geometries”, albeit with modifications relative unflavored case.