A tale of (M)2 twists

We study the parameter space of magnetically charged AdS$_2\times\mathbb{WCP}^{1}_{[n_-,n_+]}$ solutions in 4d U$(1)^4$ gauged STU supergravity. We show that both \emph{twist} and \emph{anti-twist} solutions are realised and give constraints for their existence in terms of the magnetic charges of the solution. We provide infinite families of both classes of solution in terms of their magnetic charges and weights of the orbifold. As a byproduct of our analysis we obtain a closed form expression for the free-energy of the 4-charge magnetic solution in terms of the magnetic charges and weights $n_{\pm}$. We also show that the AdS$_2$ solution is the near-horizon of an asymptotically AdS$_4$ black hole which can be found in the literature.

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