Non-rational Narain CFTs from codes over $F_4$

TL;DR

This paper introduces a novel method linking codes over $F_4$ to non-rational Narain CFTs, expanding the landscape of conformal field theories with potential for optimal spectral gaps.

Contribution

It presents a new construction connecting $F_4$ codes to non-rational Narain CFTs, complementing existing rational theory frameworks.

Findings

Constructed a map between $F_4$ codes and non-rational Narain CFTs.

Formulated a polynomial ansatz simplifying modular invariance constraints.

Achieved optimal theories with maximal spectral gaps at small central charges.

Abstract

We construct a map between a class of codes over $F_4$ and a family of non-rational Narain CFTs. This construction is complementary to a recently introduced relation between quantum stabilizer codes and a class of rational Narain theories. From the modular bootstrap point of view we formulate a polynomial ansatz for the partition function which reduces modular invariance to a handful of algebraic easy-to-solve constraints. For certain small values of central charge our construction yields optimal theories, i.e. those with the largest value of the spectral gap.