$AdS$ solutions with spindle factors

TL;DR

This work reinterpret the known AdS_3 and AdS_2 spindle solutions as spindle-structured compactifications with a spindle factor $Σ$, recasting the AdS_3 case as $AdS_3×Σ×S^1×KE_2^+$ and the AdS_2 case as $AdS_2×Σ×S^1×KE_4^+×T^2$, both arising from GK-type geometries with additional fluxes. For the $Q=0$ truncations, it performs global analyses, carries out flux quantization, and derives the holographic observable $c$ for the AdS_3 case, $c=rac{24 n_+ n_- (n_+-n_-)^2 N M}{(n_++n_-)^2}$, connecting to Donos:2008ug via a reparameterization; in the eleven-dimensional AdS_2 sector it computes seven-cycle fluxes and the Bekenstein-Hawking entropy, $S_{BH}$, with explicit dependence on topological data and flux integers. The study emphasizes that, unlike earlier minimal spindle solutions, a clear gauged-supergravity origin and dual field theories for these spindle configurations are not yet established, and it points to future avenues such as nonzero $Q$ analyses and localization to uncover the holographic duals.

Abstract

We provide the spindle interpretations of previously known solutions, $AdS_3\timesΣ\times{S}^1\times{KE}_2^+\times{T}^2$ of type IIB supergravity and $AdS_2\timesΣ\times{S}^1\times{KE}_4^+\times{T}^2$ of eleven-dimensional supergravity, where $Σ$ is a spindle factor. For the $AdS_3$ solutions, the internal space of $Σ\times{S}^1\times{KE}_2^+$ 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.