Adding Flavor to the Narain Ensemble

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.

30 pages

References in corpus (6)

• JT gravity as a matrix integral
• Averaging Over Narain Moduli Space
• Wormholes and Spectral Statistics in the Narain Ensemble
• Comments on the holographic description of Narain theories
• Kac-Moody and Virasoro Characters from the Perturbative Chern-Simons Path Integral
• Poincaré Series, 3d Gravity and Averages of Rational CFT

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• Narain to Narnia
• Chern-Simons Invariants from Ensemble Averages
• Non-rational Narain CFTs from codes over $F_4$
• Holographic description of Narain CFTs and their code-based ensembles
• Quantization of the ModMax Oscillator
• A note on ensemble holography for rational tori
• TQFT gravity and ensemble holography
• Weighed average over Narain moduli space as $T\bar{T}$ deformation of CFT target space
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• (Half) Wormholes under Irrelevant Deformation
• Higher spin wormholes from modular bootstrap
• A universal sum over topologies in 3d gravity
• Factorization and global symmetries in holography
• Algebraic Realisation of the Zamolodchikov Metric in Narain Theories
• Code CFTs and Topological Matter