Macroscopic origin of the topologically twisted index on $T^2 \times Σ_{\mathfrak{g}}$
We construct a novel family of non-supersymmetric, asymptotically locally AdS$_5$ solutions of five-dimensional minimal gauged supergravity. In Lorentzian signature the solutions describe finite temperature rotating electro-magnetically charged black strings with $S^1\times Σ_{\mathfrak{g}}$ horizon topology. In Euclidean signature the solutions are completely smooth and are asymptotic to $T^2\times Σ_{\mathfrak{g}}$. We present a detailed analysis of the thermodynamic properties of these gravitational backgrounds, compute their regularized on-shell action and analyze the extremal and supersymmetric limits. The supersymmetric, but non-extremal, limit of the Euclidean backgrounds is a family of complex black saddles and it provides the holographic dual description of the topologically twisted index of 4d $\mathcal{N}=1$ SCFTs placed on $T^2\times Σ_{\mathfrak{g}}$. We show that the supergravity regularized on-shell action in this limit is in agreement with the large $N$ limit of the topologically twisted index in the dual SCFT.