A geometric dual of \(c\)-extremization

DOI10.1007/JHEP01(2019)212zbMATH Open1409.81143arXiv1810.11026WikidataQ125618023 ScholiaQ125618023MaRDI QIDQ667315

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Publication date: 12 March 2019

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Abstract: We consider supersymmetric AdS${}_{3}imes{Y}_7$ and AdS${}_{2}imes{Y}_9$ solutions of type IIB and $D=11$ supergravity, respectively, that are holographically dual to SCFTs with $(0,2)$ supersymmetry in two dimensions and $mathcalN=2$ supersymmetry in one dimension. The geometry of $Y_{2n+1}$, which can be defined for $nge3$, shares many similarities with Sasaki-Einstein geometry, including the existence of a canonical R-symmetry Killing vector, but there are also some crucial differences. We show that the R-symmetry Killing vector may be determined by extremizing a function that depends only on certain global, topological data. In particular, assuming it exists, for $n=3$ one can compute the central charge of an AdS${}_{3}imes{Y}_7$ solution without knowing its explicit form. We interpret this as a geometric dual of $c$-extremization in $(0,2)$ SCFTs. For the case of AdS${}_{2}imes{Y}_9$ solutions we show that the extremal problem can be used to obtain properties of the dual quantum mechanics, including obtaining the entropy of a class of supersymmetric black holes in AdS${}_4$. We also study many specific examples of the type AdS${}_{3}imes{T}^{2}imes{Y}_5$, including a new family of explicit supergravity solutions. In addition we discuss the possibility that the $(0,2)$ SCFTs dual to these solutions can arise from the compactification on $T^2$ of certain $d=4$ quiver gauge theories associated with five-dimensional Sasaki-Einstein metrics and, surprisingly, come to a negative conclusion.

Full work available at URL: https://arxiv.org/abs/1810.11026

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