The holographic supersymmetric Casimir energy

We consider a general class of asymptotically locally ${\mathrm{AdS}}_5$ solutions of minimal gauged supergravity, which are dual to superconformal field theories on curved backgrounds $S^1\times M_3$ preserving two supercharges. We demonstrate that standard holographic renormalization corresponds to a scheme that breaks supersymmetry. We propose new boundary terms that restore supersymmetry, and show that for smooth solutions with topology $S^1\times {\mathbb{R}}^4$ the improved on-shell action reproduces both the supersymmetric Casimir energy and the field theory supersymmetric relation between charges.