On the Rationality and the Code Structure of a Narain CFT, and the Simple Current Orbifold

TL;DR

This paper explores the structure of Narain rational conformal field theories (RCFTs), demonstrating how they can be constructed via simple current orbifolds, and linking their partition functions to error-correcting code polynomials.

Contribution

It shows that certain Narain RCFTs are simple current orbifolds of other Narain RCFTs and connects their partition functions to code theory through polynomial representations.

Findings

Partition functions can be expressed as polynomials in q-series.

A specific case relates the polynomial to the weight enumerator of an error-correcting code.

Discrete torsion and the B-field are interconnected through the polynomial representation.

Abstract

In this paper, we discuss the simple current orbifold of a rational Narain CFT (Narain RCFT). This is a method of constructing other rational CFTs from a given rational CFT, by ``orbifolding'' the global symmetry formed by a particular primary fields (called the simple current). Our main result is that a Narain RCFT satisfying certain conditions can be described in the form of a simple current orbifold of another Narain RCFT, and we have shown how the discrete torsion in taking that orbifold is obtained. Additionally, the partition function can be considered a simple current orbifold with discrete torsion, which is determined by the lattice and the B-field. We establish that the partition function can be expressed as a polynomial, with the variables substituted by certain q-series. In a specific scenario, this polynomial corresponds to the weight enumerator polynomial of an error-correcting code. Using this correspondence to the code theory, we can relate the B-field, the discrete torsion, and the B-form to each other.