Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Shift orbifolds, decompactification limits, and lattices

Dan Israel, Ilarion V. Melnikov, Yann Proto

TL;DR

This work develops a comprehensive lattice-based framework for shift orbifolds of Narain CFTs, with a detailed treatment of heterotic theories, decompactification limits, and dualities. By encoding orbifold actions with shift vectors and vacuum parameters, it derives consistency criteria, connects with Gannon’s shifting method, and explains when a shift interchanges the two ten-dimensional heterotic lattices. The analysis extends to nine-dimensional moduli spaces, T-dualities, and explicit low-order cyclic shifts, and then generalizes to Niemeier/CFTs, including the Leech lattice, via deep-hole and Borcherds constructions. The results illuminate the interplay between orbifold CFTs and lattice theory, providing practical algorithms to classify shift orbifolds and insights into duality frames across heterotic moduli spaces.

Abstract

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 the Leech lattice and its shift orbifolds.

Shift orbifolds, decompactification limits, and lattices

TL;DR

This work develops a comprehensive lattice-based framework for shift orbifolds of Narain CFTs, with a detailed treatment of heterotic theories, decompactification limits, and dualities. By encoding orbifold actions with shift vectors and vacuum parameters, it derives consistency criteria, connects with Gannon’s shifting method, and explains when a shift interchanges the two ten-dimensional heterotic lattices. The analysis extends to nine-dimensional moduli spaces, T-dualities, and explicit low-order cyclic shifts, and then generalizes to Niemeier/CFTs, including the Leech lattice, via deep-hole and Borcherds constructions. The results illuminate the interplay between orbifold CFTs and lattice theory, providing practical algorithms to classify shift orbifolds and insights into duality frames across heterotic moduli spaces.

Abstract

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 the Leech lattice and its shift orbifolds.

Paper Structure

This paper contains 18 sections, 101 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Conventions and notation for Narain CFT
  3. Lattice set up
  4. Vertex operators
  5. Symmetries of the Narain CFT
  6. General shift orbifolds
  7. Orbifold consistency conditions
  8. Relation to the "shifting method"
  9. The quantum symmetry
  10. Dualities among shift vectors
  11. Heterotic shift orbifolds
  12. A nine-dimensional perspective
  13. The heterotic moduli space
  14. Decompactification limits and T-dualities
  15. Cyclic shift orbifolds of low order
  16. ...and 3 more sections

Figures (1)

  • Figure 1: The $2$-neighborhood graph of Niemeier lattices.