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Adding Flavor to the Narain Ensemble
- Publication Year :
- 2021
-
Abstract
- 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.<br />Comment: 30 pages
- Subjects :
- High Energy Physics - Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2102.12509
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/JHEP05(2022)090