A tale of (M)2 twists

TL;DR

This paper explores the parameter space of magnetically charged AdS$_2$ solutions in 4d supergravity, identifying conditions for twist and anti-twist solutions, and deriving their free energy expressions.

Contribution

It provides a comprehensive analysis of twist and anti-twist solutions, offering infinite families and a closed-form free energy expression in terms of magnetic charges.

Findings

Both twist and anti-twist solutions are realized.

Infinite families of solutions are constructed.

A closed-form expression for free energy is derived.

Abstract

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.