%ADatta, Shouvik%ADuary, Sarthak%AKraus, Per%AMaity, Pronobesh%AMaloney, Alexander%BJournal Name: Journal of High Energy Physics; Journal Volume: 2022; Journal Issue: 5
%D2022%I
%JJournal Name: Journal of High Energy Physics; Journal Volume: 2022; Journal Issue: 5
%K
%MOSTI ID: 10345751
%PMedium: X
%TAdding flavor to the Narain ensemble
%XA 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.
%0Journal Article