## Abstract

We consider supersymmetric AdS_{3} × Y_{7} and AdS_{2} × 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 N = 2 supersymmetry in one dimension. The geometry of Y_{2n+1}, which can be defined for n ≥ 3, 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} × 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} × 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} × T^{2} × 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.

Original language | English |
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Article number | 212 |

Number of pages | 54 |

Journal | Journal of High Energy Physics |

Volume | 2019 |

Issue number | 1 |

DOIs | |

Publication status | Published - 29 Jan 2019 |

## Keywords

- AdS-CFT Correspondence
- Black Holes in String Theory
- Differential and Algebraic Geometry
- Supersymmetric Gauge Theory

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