Gluing two discs into a spindle

TL;DR

This paper constructs new supergravity solutions involving discs (half-spindles), computes associated anomaly polynomials, and introduces a method to derive central charges of dual field theories by gluing gravitational blocks.

Contribution

It introduces a novel class of AdS$_5 imes ext{disc}$ solutions in 7D supergravity, computes their anomaly polynomials, and develops a gluing procedure for gravitational blocks to obtain central charges.

Findings

Constructed AdS$_5 imes$ disc solutions in 7D supergravity.

Computed off-shell central charges from anomaly polynomials.

Developed a gluing method to combine gravitational blocks for discs.

Abstract

We construct AdS$_5 \times \Sigma$ solutions of $D=7$ gauged supergravity where $\Sigma$ 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 $\Sigma$ 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.