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PreprintCC BY 4.0arXiv

The A3 Narain family over ℤ4

  • Rajae Sammani
  • Abdellah Sebbar
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Abstract

The code {000,220,202,022}⊂ℤ43 realizes the split A3 root-weight gluing construction as ordinary Construction A, preserving the Lorentzian pairing and the positive energy form. For two hyperbolic pairs of A3 blocks, the twenty-two even self-dual gluing codes form seven block-monomial classes. Explicit metric and B-field representatives and theta series distinguish exactly seven T-duality classes in this family at central charge six; the one-pair family has two classes at central charge three. For arbitrary d, the chiral root system on either side is A13m, where m counts the words (2ei,2ei) in the gluing code. Exactly one two-pair class has no zero-B T-duality frame. Intersections of gluing codes determine finite shift orbifolds between the backgrounds, with the target code specifying the twisted-sector projections.

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Cite

BibTeXRIS
BibTeX
@misc{sammani2026narain,
  title = {{The $A_3$ Narain family over $\mathbbZ_4$}},
  author = {Rajae Sammani and Abdellah Sebbar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26610},
  eprint = {2610.26610},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26610},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The A_3 Narain family over ℤ_4
AU  - Rajae Sammani
AU  - Abdellah Sebbar
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26610
UR  - https://arxiv.org/abs/2610.26610
AB  - The code {000,220,202,022}⊂ℤ_4^3 realizes the split A_3 root-weight gluing construction as ordinary Construction A, preserving the Lorentzian pairing and the positive energy form. For two hyperbolic pairs of A_3 blocks, the twenty-two even self-dual gluing codes form seven block-monomial classes. Explicit metric and B-field representatives and theta series distinguish exactly seven T-duality classes in this family at central charge six; the one-pair family has two classes at central charge three. For arbitrary d, the chiral root system on either side is A_1^3m, where m counts the words (2e_i,2e_i) in the gluing code. Exactly one two-pair class has no zero-B T-duality frame. Intersections of gluing codes determine finite shift orbifolds between the backgrounds, with the target code specifying the twisted-sector projections.
ER  -