Comments on the holographic description of Narain theories

• Published in: The journal of high energy physics 2021-10, Vol.2021 (10), p.1-26, Article 197
• Main Authors: Dymarsky, Anatoly, Shapere, Alfred
• Format: Article
• Language: English
• Subjects: AdS-CFT Correspondence; Black holes; Charge density; Chern-Simons Theories; Classical and Quantum Gravitation; Conformal Field Theory; Consistency; Density of states; Elementary Particles; Gravitation theory; Gravity; High energy physics; Holography; Hypotheses; Models of Quantum Gravity; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP10(2021)197

A bstract We discuss the holographic description of Narain U(1) c × U(1) c conformal field theories, and their potential similarity to conventional weakly coupled gravitational theories 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 ∆ 1 = c /(2 πe ). 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.