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Adding flavor to the Narain ensemble

https://doi.org/10.1007/JHEP05(2022)090

Datta, Shouvik ; Duary, Sarthak ; Kraus, Per ; Maity, Pronobesh ; Maloney, Alexander ( May 2022 , Journal of High Energy Physics)

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