$AdS$ solutions with spindle factors

TL;DR

This paper interprets certain known supergravity solutions as spindle geometries, computes flux quantizations, and derives holographic central charges and entropies, expanding understanding of these solutions' dual field theories.

Contribution

It provides spindle interpretations for specific $AdS$ solutions and performs flux quantizations and entropy calculations, which were not previously established.

Findings

Flux quantizations performed for the solutions.

Holographic central charges calculated.

Bekenstein-Hawking entropy estimated.

Abstract

We provide the spindle interpretations of previously known solutions, $AdS_3\times\Sigma\times{S}^1\times{KE}_2^+\times{T}^2$ of type IIB supergravity and $AdS_2\times\Sigma\times{S}^1\times{KE}_4^+\times{T}^2$ of eleven-dimensional supergravity, where $\Sigma$ is a spindle factor. For the $AdS_3$ solutions, the internal space of $\Sigma\times{S}^1\times{KE}_2^+$ was previously known as the $\mathscr{Y}^{p,q}$ manifold, which shares the identical topology of the $Y^{p,q}$ manifolds. Unlike the previously known spindle solutions, the gauged supergravity origin and the field theory dual of the solutions are not clear at the moment. We perform the flux quantizations and calculate the holographic central charge and the Bekenstein-Hawking entropy of the presumed black hole solutions, respectively.