Ground State Degeneracy in the Twisted Sectors of Conway Moonshine

Abstract

We discover a new and unexpected pattern in the ground state degeneracy of the N = 1 Conway Moonshine SVOA twisted sectors. The main goal of this thesis is to calculate the NS- and R- characters of the Co0-twisted R-sector of Conway Moonshine. We find empirically that in Conway Moonshine, for about 95% of possible Co0-twistings, all ground states have the same fermionic parity, whereas 5% of them have ground states of bosonic and fermionic parities. We prove that the characters of the Ramondsector twisted by an action of Co0 must be constant. Additionally, we prove that the Ramond-character of the g-twisted R-sector is equal to the trace of g.