Elliptic genera from classical error-correcting codes

TL;DR

This paper develops a systematic method to compute elliptic genera of chiral fermionic conformal field theories derived from classical error-correcting codes, linking coding theory with supersymmetric quantum field theory.

Contribution

It introduces a novel approach to calculate elliptic genera from classical codes using the U(1) current in N=2 superconformal algebra, and constructs explicit examples for small central charges.

Findings

Constructed extremal N=2 elliptic genera from classical codes.

Decomposed near-extremal elliptic genera into superconformal characters.

Provided a framework connecting error-correcting codes with supersymmetric conformal field theories.

Abstract

We consider chiral fermionic conformal field theories constructed from classical error-correcting codes and provide a systematic way of computing their elliptic genera. We exploit the $\mathrm{U}(1)$ current of the $\mathcal{N}=2$ superconformal algebra to obtain the $\mathrm{U}(1)$-graded partition function that is invariant under the modular transformation and the spectral flow. We demonstrate our method by constructing extremal $\mathcal{N}=2$ elliptic genera from classical codes for relatively small central charges. Also, we give near-extremal elliptic genera and decompose them into $\mathcal{N}=2$ superconformal characters.