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  1. A<sc>bstract</sc>

    We compute the ZZ annulus one-point function of the cosmological constant operator in non-critical string theory, regulating divergences from the boundaries of moduli space using string field theory. We identify a subtle issue in a previous analysis of these divergences, which was done in the context of thec= 1 string theory, and where it had led to a mismatch with the prediction from the dual matrix quantum mechanics. After fixing this issue, we find a precise match to the expected answer in both thec< 1 andc= 1 cases. We also compute the disk two-point function, which is a quantity of the same order, and show that it too matches with the general prediction.

     
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  2. 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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