D3-Branes Wrapped on a Spindle

Abstract

We construct supersymmetric AdS 5 × Σ solutions of D = 7 gauged supergravity, where Σ is a two-dimensional orbifold known as a spindle. These uplift on S 4 to solutions of D = 11 supergravity which have orbifold singularites. We argue that the solutions are dual to d = 4, 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.

Rotating multi-charge spindles and their microstates

“…in the two-dimensional theory [3,15,16]. The two-dimensional anomaly polynomial in the case of the static spindle with a single magnetic flux was derived in [12]. Here, we generalize the derivation to the case of general magnetic charges and of general background fields for the flavor charges.…”

“…In this paper we extend our analysis to another class of supersymmetric AdS 3 vacua in type IIB string theory which are based on D3-branes wrapped on a spindle, i.e. the one-dimensional complex weighted projective space, WP 1 [n 1 ,n 2 ] , which is an orbifold with spherical topology and two conical singularities at the poles [8][9][10][11][12]. An example of this class of solutions was originally found in [8] and later generalized in [9] working in ten dimensions.…”

“…[n 1 ,n 2 ] supersymmetric solution of minimal gauged supergravity found in [10] and generalized in [11] to the case of multiple charges. Supersymmetry is realized through a magnetic flux along the spindle but the theory is not topologically twisted [12]. Notably, the full ten-dimensional metric is completely regular, i.e.…”

“…Notably, the full ten-dimensional metric is completely regular, i.e. the apparent conical singularities in five dimensions are smoothed out by the embedding of the spindle inside a seven-dimensional geometry [11,12]. The authors of [10,11] described these solutions as potential horizons of "unbalanced spherical black rings".…”

“…The authors of [10,11] described these solutions as potential horizons of "unbalanced spherical black rings". More recently the authors of [12] successfully pursued the interpretation in terms of N = 4 super Yang-Mills (SYM) theory wrapped on the spindle which gives rise to a two-dimensional N = (0, 2) conformal field theory (CFT). Quite remarkably, despite the presence of singularities, they were able to match the central charge computed holographically with the result obtained from integrating the anomaly polynomial of N = 4 SYM on WP 1 [n 1 ,n 2 ] .…”