Abstract
We study the parameter space of magnetically charged AdS2× {mathbbm{WCP}}_{left[{n}_{-}{n}_{+}right]}^1 solutions in 4d U(1)4 gauged STU supergravity. We show that both twist and 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±. We also show that the AdS2 solution is the near-horizon of an asymptotically AdS4 black hole which can be found in the literature.
Highlights
For the M5-brane and D4-brane geometries, supersymmetry is preserved by yet another mechanism, [4, 11] dubbed a topological topological twist, or twist on
We show that the AdS2 solution is the near-horizon of an asymptotically AdS4 black hole which can be found in the literature
We have studied the possibility of realising both the twist and anti-twist for the multicharge AdS2 × WCP1[n+,n] solutions
Summary
We will perform some clever manipulations of the roots of the polynomial f (w) which allows us to write the roots in terms of the charges and n± whilst eliminating the constants cI , by the end of this section these will not appear again in this paper. Recalling that we take w3 > 0 without loss of generality, the two types of twist are realised when w2 < 0 < w3 ,. To cover both cases let us use the parameter σ = ±1 introduced earlier to write σw2 = |w2|. The P(a) combinations are the ones which involve the integer magnetic charges and which we are interested in expressing everything in terms of, in the intermediate computations the Q(a) will be most useful. The combinations P(a) are the natural combinations arising from the quartic invariant for the STU model when considering a purely electric gauging with only magnetic charges.
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