Related papers: Unifying error-correcting code/Narain CFT correspo…
We study error correcting codes that construct the Narain lattices of heterotic strings as code lattices. We identify, in both $E_8\times E_8$ and Spin$(32)/Z_2$ heterotic strings, a pair of a binary code and a set of the corresponding…
There is a rich connection between classical error-correcting codes, Euclidean lattices, and chiral conformal field theories. Here we show that quantum error-correcting codes, those of the stabilizer type, are related to Lorentzian lattices…
We construct Narain conformal field theories (CFTs) from quantum subsystem codes, a more comprehensive class of quantum error-correcting codes than quantum stabilizer codes, for qudit systems of prime dimensions. The resulting code CFTs…
We generalize the construction of Narain conformal field theories (CFTs) from qudit stabilizer codes to the construction from quantum stabilizer codes over the finite field of prime power order ($\mathbb{F}_{p^m}$ with $p$ prime and $m\geq…
We construct Narain CFTs from self-dual codes on the finite field $F_p$ through even self-dual lattices for any prime $p>2$. Using this correspondence, we can relate the spectral gap and the partition function of the CFT to the error…
We give new results on the structure and representations of the three lattices $\mathbf{\Lambda }_{\mathrm{k}},\mathbf{\Lambda }_{\mathrm{k}\mathcal{C}},\mathbf{\Lambda }_{\mathrm{k}}^{\ast }$ relevant to code CFTs realizing Narain…
We investigate the gauging of a $\mathbb{Z}_N$ symmetry in lattice conformal field theories (CFTs), also known as Narain CFTs. For prime $N$, we derive a spin selection rule for operators in a $\mathbb{Z}_N$ charge-twisted sector of a…
In this paper, we propose a novel framework for modeling topological phases of matter using code-based Narain conformal field theories (NCFTs). We show that the algebraic structure of the NCFTs naturally embeds into critical lattice quantum…
We give a general construction relating Narain rational conformal field theories (RCFTs) and associated 3d Chern-Simons (CS) theories to quantum stabilizer codes. Starting from an abelian CS theory with a fusion group consisting of $n$…
We construct a discrete subset of Narain CFTs from quantum stabilizer codes with qudit (including qubit) systems whose dimension is a prime number. Our construction exploits three important relations. The first relation is between qudit…
We investigate the gauging of a $\mathbb{Z}_2$ symmetry in Narain conformal field theories (CFTs) constructed from qudit stabilizer codes. Considering both orbifold and fermionization, we establish a connection between $\mathbb{Z}_2$…
Code CFTs are 2d conformal field theories defined by error-correcting codes. Recently, Dymarsky and Shapere generalized the construction of code CFTs to include quantum error-correcting codes. In this paper, we explore this connection at…
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.…
We consider chiral fermionic conformal field theories (CFTs) constructed from lattices and investigate their orbifolds under reflection and shift $\mathbb{Z}_2$ symmetries. For lattices based on binary error-correcting codes, we show the…
Recently established connection between additive codes and Narain CFTs provides a new tool to construct theories with special properties and solve modular bootstrap constraints by reducing them to algebraic identities. We generalize…
We revisit Narain conformal field theories from an algebraic perspective based on finite dimensional Lie algebras $\mathbf{g}$ and representations $\mathcal{R}_{\mathbf{g}}$, and show how the root and weight lattices can encode the momenta…
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…
We propose a lattice construction from totally real and CM fields, which naturally generalizes the Construction A of lattices from $p$-ary codes obtained from the cyclotomic field $\mathbb{Q}(\zeta_p)$, $p$ a prime, which in turn contains…
We describe the general shift orbifold of a Narain CFT and use this to investigate decompactification limits in the heterotic Narain moduli space. We also comment on higher rank theories and describe some applications to the CFT based on…
We provide a precise relation between an ensemble of Narain conformal field theories (CFTs) with central charge $c=n$, and a sum of $(U(1) \times U(1))^n$ Chern-Simons theories on different handlebody topologies. We begin by reviewing the…