Comments on the holographic description of Narain theories

Abstract

We discuss the holographic description of Narain $U(1{)}^c\times U(1{)}^c$ conformal field theories, and their potential similarity to conventional weakly coupled gravity in the bulk, in the sense that the effective IR bulk description includes "$U(1)$ gravity" amended with additional light degrees of freedom. Starting from this picture, we formulate the hypothesis that in the large central charge limit the density of states of any Narain theory is bounded by below by the density of states of $U(1)$ gravity. This immediately implies that the maximal value of the spectral gap for primary fields is ${\Delta }_1=c/(2\pi e)$. To test the self-consistency of this proposal, we study its implications using chiral lattice CFTs and CFTs based on quantum stabilizer codes. First we notice that the conjecture yields a new bound on quantum stabilizer codes, which is compatible with previously known bounds in the literature. We proceed to discuss the variance of the density of states, which for consistency must be vanishingly small in the large-$c$ limit. We consider ensembles of code and chiral theories and show that in both cases the density variance is exponentially small in the central charge.

arXiv commentv2, journal version with typos corrected

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Cited by in corpus (20)

• Wormholes and Spectral Statistics in the Narain Ensemble
• Adding Flavor to the Narain Ensemble
• Narain CFTs and error-correcting codes on finite fields
• Narain CFTs and Quantum Codes at Higher Genus
• Fermionic CFTs from classical codes over finite fields
• Classical Codes and Chiral CFTs at Higher Genus
• Holographic description of Narain CFTs and their code-based ensembles
• Relation between spectra of Narain CFTs and properties of associated boolean functions
• A note on ensemble holography for rational tori
• TQFT gravity and ensemble holography
• Global Symmetries, Code Ensembles, and Sums Over Geometries
• Weighed average over Narain moduli space as $T\bar{T}$ deformation of CFT target space
• Fluctuating Ensemble Averages and the BTZ Threshold
• Wormholes and surface defects in rational ensemble holography
• (Half) Wormholes under Irrelevant Deformation
• Fermionic CFTs from topological boundaries in abelian Chern-Simons theories
• Code CFTs and Topological Matter
• Optimal Narain CFTs from Codes
• Algebraic constructions of code lattices in Narain conformal field theories
• Algebraic Realisation of the Zamolodchikov Metric in Narain Theories