Orbifolds of chiral fermionic CFTs and their duality

TL;DR

This paper explores orbifolds of chiral fermionic CFTs derived from lattices, revealing dualities via code-based structures and computing their partition functions, with applications in supersymmetry and symmetry-breaking.

Contribution

It introduces a novel code-based approach to analyze orbifolds of chiral fermionic CFTs and uncovers dualities between reflection and shift orbifolds.

Findings

Duality between reflection and shift orbifolds established

Partition functions computed for binary and nonbinary codes

Applications in constructing supersymmetric and symmetry-free CFTs

Abstract

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 duality between reflection and shift orbifolds using a triality structure inherited from the binary codes. Additionally, we systematically compute the partition functions of the orbifold theories for both binary and nonbinary codes. Finally, we explore applications of this code-based construction in the search for supersymmetric CFTs and chiral fermionic CFTs without continuous symmetries.