Supersymmetric spindles

TL;DR

This paper explores supersymmetric geometries based on spindle orbifolds in holography, classifying spinor solutions, constructing supergravity duals for branes wrapping spindles, and analyzing their field theory implications.

Contribution

It identifies two main classes of supersymmetric spindle geometries, constructs explicit supergravity solutions for D3, M2, and M5 branes, and connects these to dual field theories and anomaly calculations.

Findings

Classified spin$^c$ spinors into twist and anti-twist cases.

Constructed supergravity solutions for D3, M2, and M5 branes on spindles.

Reproduced central charge from anomaly polynomial for D3-branes.

Abstract

In the context of holography, we analyse aspects of supersymmetric geometries based on two-dimensional orbifolds known as spindles. By analysing spin$^c$ spinors on a spindle with an azimuthal rotation symmetry we show that under rather general conditions there are just two possibilities, called the `twist' and the `anti-twist', which are determined by the quantized magnetic flux through the spindle. A special case of the twist is the standard topological twist which is associated with constant and chiral spinors. We construct solutions of $D=5$ and $D=4$ STU gauged supergravity theories that are dual to D3-branes and M2-branes wrapping spindles, respectively, which realize both the anti-twist, as seen before, but also the twist. For the wrapped D3-brane solutions we reproduce the central charge of the gravity solution from the dual field theory by analysing the anomaly polynomial of $\mathcal{N}=4$ SYM theory. We also discuss M5-branes wrapped on spindles both from a gravity and a field theory point of view.