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We calculate the ground state degeneracies of all twisted sectors in the"Conway Moonshine'' holomorphic SCFT $V^{f\natural}$. We find that almost allsectors have ground states of only a single parity: specifically, 66 twistedsectors have nontrivial ground states of a single parity, 39 twisted sectorshave spontaneous supersymmetry breaking, and only 6 twisted sectors have groundstates of both parities. Although "nontrivial ground states, all of the sameparity'' is the expected behaviour for a generic SQM model without symmetryprotection, it is surprising in the presence of a large symmetry group, as isthe case in $V^{f\natural}$. This surprise hints that there areas-yet-undiscovered features of Conway Moonshine.

Ground-state degeneracy of twisted sectors of Conway Moonshine SCFT