Gluing two discs into a spindle

TL;DR

The paper addresses holographic duals of disc (half-spindle) compactifications in $AdS_5$ from M5-branes by computing the $D=6$ M5 anomaly polynomial and reducing it on a disc to obtain an off-shell central charge for the dual $D=4$, $\mathcal{N}=1$ SCFT. The central idea is to decompose disc contributions into gravitational blocks associated with the disc center and boundary, and then glue two discs with opposite orientation to recover the known spindle central charge, providing a novel gravitational-block framework for discs. The authors perform an explicit uplift to $D=11$ and verify the central charge against the gravity calculation, highlighting a new boundary-block contribution and the conditions under which boundary terms cancel in the glued configuration. The work suggests connections to equivariant localization with boundaries and potential class $\mathcal{S}$ interpretations, offering a path to systematic construction of spindle duals from disc building blocks and stimulating further study of boundary effects in holography.

Abstract

We construct AdS$_5 \times Σ$ solutions of $D=7$ gauged supergravity where $Σ$ is a disc, also known as a half-spindle, and uplift them to $D=11$ supergravity. By computing the anomaly polynomial of the M5-brane theory compactified on $Σ$ in the large $N$ limit, we obtain the off-shell central charges of the dual $D=4$, $\mathcal{N}=1$ superconformal field theory to disc solutions. These off-shell central charges decompose into contributions from the center and the boundary of the disc and are referred to as the gravitational blocks for disc. By suitably gluing the gravitational blocks for two discs along their boundaries, we reproduce the off-shell central charge for a single spindle.