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2021

Adding Flavor to the Narain Ensemble

Datta, Shouvik, Duary, Sarthak, Kraus, Per et al.

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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.

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