Optimal Narain CFTs from Codes

TL;DR

This paper demonstrates that all known optimal Narain conformal field theories can be constructed from additive codes, and introduces new theories with spectral gaps that grow linearly with central charge, approaching theoretical bounds.

Contribution

It generalizes the code-based construction of Narain CFTs to include all known optimal theories and conjectures universality for all central charges.

Findings

All known optimal Narain theories can be constructed from codes.

Code theories with spectral gap growing linearly with central charge c.

Spectral gap coefficient saturates the conjectural upper bound.

Abstract

Recently established connection between additive codes and Narain CFTs provides a new tool to construct theories with special properties and solve modular bootstrap constraints by reducing them to algebraic identities. We generalize previous constructions to include many new theories, in particular we show that all known optimal Narain theories, i.e. those maximizing the value of spectral gap, can be constructed from codes. For asymptotically large central charge $c$ we show there are code theories with the spectral gap growing linearly with $c$, with the coefficient saturating the conjectural upper bound. We therefore conjecture that optimal Narain theories for any value of $c$ can be obtained from codes.