Extremal chiral $\mathcal N=4$ SCFT with $c=24$

TL;DR

This paper constructs a new extremal chiral $ =4$ superconformal field theory with central charge 24 using a $z_2$ orbifold of a lattice theory based on the Niemeier lattice $A_2^{12}$, revealing connections to sporadic groups.

Contribution

It introduces a novel extremal chiral $ =4$ SCFT at $c=24$ derived from a Niemeier lattice, expanding the landscape of known extremal theories.

Findings

Constructed an extremal chiral $ =4$ SCFT with $c=24$.

Identified a discrete symmetry group related to $M_{11}$.

Connected to previous extremal theories with different supersymmetries.

Abstract

We construct an extremal chiral $\mathcal N=4$ superconformal field theory with central charge 24 from a $\mathbb Z_2$ orbifold of the chiral bosonic theory with target $\mathbb R^{24}/\Lambda$, where $\Lambda$ is the Niemeier lattice with root system $A_2^{12}$. This construction is analogous to constructions of extremal chiral $\mathcal N=1$ and $\mathcal N=2$ CFTs with $c=24$, where $\Lambda = \Lambda_{Leech}$ and the Niemeier lattice with root system $A_1^{24}$, respectively. The theory has a discrete symmetry group related to the sporadic group $M_{11}$.