M5-branes wrapped on a spindle

Abstract

We construct supersymmetric AdS5 × Σ solutions of D = 7 gauged supergravity, where Σ is a two-dimensional orbifold known as a spindle. These uplift on S4 to solutions of D = 11 supergravity which have orbifold singularites. We argue that the solutions are dual to d = 4, $$ \mathcal{N} $$ N = 1 SCFTs that arise from N M5-branes wrapped on a spindle, embedded as a holomorphic curve inside a Calabi-Yau three-fold. In contrast to the usual topological twist solutions, the superconformal R-symmetry mixes with the isometry of the spindle in the IR, and we verify this via a field theory calculation, as well as reproducing the gravity formula for the central charge.

Supersymmetric spindles

“…The only other assumption that goes into the proof is that the Killing spinor should be non-vanishing at these orbifold points, which holds on general grounds for supersymmetric AdS solutions, as we shall discuss. Our analysis also clarifies why the regularity arguments that have been used for supergravity solutions with spindles constructed in [1][2][3][4][5][6][7][8] do in fact give the correct results.…”

“…3 Moreover, these twist solutions have a natural physical interpretation as the IR limit of D3-branes and M2-branes wrapped on a spindle that is holomorphically embedded inside a Calabi-Yau four-fold and five-fold, respectively. Interestingly, for AdS 5 ×Σ M5-brane solutions the construction in [6] only leads to twist solutions, while for AdS 3 × Σ × Σ g M5-brane solutions we find new twist solutions, as well as the previously known anti-twist solutions. It is an interesting open problem to identify a UV geometry for the many anti-twist solutions that have now been constructed, involving wrapped branes, a point we discuss further in section 6.…”

“…Section 4 presents a similar analysis for AdS 2 × Σ M2-brane solutions, although here the regularity conditions are more difficult to solve in closed form, and we content ourselves with showing that new twist solutions exist, without classifying them. In section 5 we briefly discuss AdS 5 × Σ M5-brane solutions, in particular constructing the explicit Killing spinors for the solutions found in [6]. We conclude with some discussion in section 6.…”

“…As already mentioned, several different classes of supersymmetric supergravity solutions involving spindles have recently been constructed, including [1,[3][4][5][6][7][8]. Typically these are realized as solutions to a lower-dimensional gauged supergravity theory, and then uplifted to D = 10 string theory or D = 11 M-theory solutions, where the solutions describe D3-brane, M2-brane or M5-brane backgrounds.…”

“…to be a weighted projective space that is specified by two positive, co-prime integers n 1 , n 2 . Various AdS×Σ supersymmetric solutions of gauged supergravity theories in D = 4, 5 and 7 dimensions have now been constructed, which are naturally associated with 1 M2, D3 and M5-branes, respectively [1,[3][4][5][6][7][8]. These can then be uplifted on certain compact manifolds to give supersymmetric solutions of D = 10 and D = 11 supergravity that are dual to new SCFTs.…”