Supersymmetric conformal field theories from quantum stabilizer codes

TL;DR

This paper introduces a method to construct fermionic conformal field theories using quantum stabilizer codes, enabling the systematic search for supersymmetric theories, including those with $ =4$ supersymmetry.

Contribution

It develops a novel approach linking quantum stabilizer codes to fermionic CFTs and establishes criteria for supersymmetry, including explicit examples with $ =4$ supersymmetry.

Findings

Constructed fermionic CFTs from quantum stabilizer codes.

Derived criteria for supersymmetry in these theories.

Identified codes realizing $ =4$ supersymmetry.

Abstract

We construct fermionic conformal field theories (CFTs) whose spectra are characterized by quantum stabilizer codes. We exploit our construction to search for fermionic CFTs with supersymmetry by focusing on quantum stabilizer codes of the Calderbank-Shor-Steane type, and derive simple criteria for the theories to be supersymmetric. We provide several examples of fermionic CFTs that meet the criteria, and find quantum codes that realize $\mathcal{N} =4$ supersymmetry. Our work constitutes a new application of quantum codes and paves the way for the methodical search for supersymmetric CFTs.