Comments on the holographic description of Narain theories

Understand

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.