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

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.

Theorems & Definitions (18)

• Theorem 2.1: A part of Theorem 4.5.2 of wendland2000moduli
• Definition 2.1
• Proposition 3.1
• Lemma 3.1
• proof
• Lemma 3.2
• proof
• proof : Proof of Prop.\ref{['prop3.1']}
• Theorem 3.1
• proof