A tale of (M)2 twists

Abstract

We study the parameter space of magnetically charged AdS2×$$ {\mathbbm{WCP}}_{\left[{n}_{-}{n}_{+}\right]}^1 $$ WCP n − n + 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.

M5-branes wrapped on four-dimensional orbifolds

“…More precisely we consider (SU(2) × SU(2))/Z 2 ∼ = SO(4) ⊂ SO(5) and then embed the two U(1)'s via [U(1) ⊂ SU(2)] 2 . The bosonic field content consists of the D = 7 metric, two gauge fields A 12 (1) , A 34 (1) with field strengths F 12 (2) , F 34 (2) , two scalar fields λ i , and a three-form S 5 (3) . The Lagrangian is given by…”

“…with p i ∈ Z. Thus, A 12 (1) and A 34 (1) are connection one-forms on line bundles O(p 1 ) and O(p 2 ) over Σ 2 , respectively, and, using (2.6), the R-symmetry gauge field A 12 (1)…”

“…Firstly, as expected, the suitably normalised D = 5 gauge field A (1) appears in the ansatz in a manner that is associated with gauging constant shifts of the φ coordinate: dφ → dφ − 4 3 A (1) . Interestingly, we find that this needs to be done using the specific gauge choice 6 for the gauge fields A 12 (1) , A 34…”

“…More precisely, here one can regard S 4 ⊂ R ⊕ C ⊕ C, with w 0 a coordinate on the first factor, and (w i , χ i ) being polar coordinates on the two copies of C, i = 1, 2. The two factors of C are then fibred over the seven-dimensional spacetime via the U(1) gauge fields A 12 (1) , A 34 (1) , respectively. As such, this fibration is well-defined only if the periods of the corresponding gauge field fluxes F 12 (2) ≡ dA 12 (1) , F 34 (2) ≡ dA 34 (1) are appropriately quantised through two-cycles in the base AdS 3 × M 4 .…”

“…In a recent development, starting with [3], it has been appreciated that there are more general constructions in which the branes wrap a spindle, a two-dimensional orbifold with quantised deficit angles at the two poles. The first examples considered D3-branes wrapping spindles [3], but constructions involving M2-branes, M5-branes and D4-branes have now also been made [4][5][6][7][8][9][10][11][12]. These new AdS/CFT examples, which have been studied both from a gravity and a field theory point of view, have a number of interesting features.…”