Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Error correcting codes and heterotic Narain CFTs

Shun'ya Mizoguchi, Takumi Oikawa

Abstract

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 metric, B field, and background gauge field, such that the lattice constructed from the binary code by Construction A coincides with the Narain lattice. We also construct heterotic Narain lattices using codes over $F_3$ and $F_5$ by Construction A${}_C$ and "Construction A${}_g$" with $g=SU(5)$, respectively. As a bi-product, we also clarify the relationship between codes that construct Euclidean even self-dual lattices and NSR-fermions, where the $Z_2$ inversion structure of the generator matrices plays a significant role.

Error correcting codes and heterotic Narain CFTs

Abstract

We study error correcting codes that construct the Narain lattices of heterotic strings as code lattices. We identify, in both and Spin heterotic strings, a pair of a binary code and a set of the corresponding metric, B field, and background gauge field, such that the lattice constructed from the binary code by Construction A coincides with the Narain lattice. We also construct heterotic Narain lattices using codes over and by Construction A and "Construction A" with , respectively. As a bi-product, we also clarify the relationship between codes that construct Euclidean even self-dual lattices and NSR-fermions, where the inversion structure of the generator matrices plays a significant role.
Paper Structure (10 sections, 78 equations)

This paper contains 10 sections, 78 equations.

Table of Contents

  1. Introduction
  2. Heterotic Narain lattice
  3. Heterotic Narain lattice constructed from binary codes
  4. Example
  5. Heterotic Narain lattice constructed from codes over $\hbox{F}_3$
  6. Heterotic Narain lattice constructed from codes over $\hbox{F}_5$
  7. Conclusion and discussion
  8. Codes constructing the $D_{16}^+$ lattice and NSR fermions
  9. Extended Hamming code $e_8$ to the $E_8$ lattice
  10. Binary codes constructing the $D_{16}^+$ lattice