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

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 $M_{11}$.