Comments on the holographic description of Narain theories

We discuss the holographic description of Narain U(1)(c) x 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 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.

Automated summary

This study discusses the holographic description of Narain U(1)(c) x U(1)(c) conformal field theories, proposing a hypothesis that the density of states of any Narain theory in the large central charge limit is bounded by the density of states of U(1) gravity. Testing this proposal using chiral lattice CFTs and CFTs based on quantum stabilizer codes reveals new bounds on quantum stabilizer codes and the exponentially small density variance in the central charge limit.