A positive energy theorem for AdS solitons

The uncharged AdS₄ soliton has been recently shown to be continuously connected to a magnetic, supersymmetric AdS₄ soliton within N=8 gauged supergravity. By constructing the asymptotic superalgebra, we establish a positive energy theorem for the magnetic AdS₄ solitons admitting well-defined asymptotic Killing spinors, antiperiodic on a contractible S¹. We show that there exists only one discrete solution endowed with these boundary conditions satisfying the bound, the latter being saturated by the null energy supersymmetric configuration. Despite having negative energy, the uncharged AdS₄ soliton does not contradict the positive energy theorem, as it does not admit well-defined asymptotic Killing spinors.