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Journal of High Energy Physics

, 2019:212 | Cite as

A geometric dual of c-extremization

  • Christopher Couzens
  • Jerome P. GauntlettEmail author
  • Dario Martelli
  • James Sparks
Open Access
Regular Article - Theoretical Physics
  • 15 Downloads

Abstract

We consider supersymmetric AdS3 × Y7 and AdS2 × Y9 solutions of type IIB and D = 11 supergravity, respectively, that are holographically dual to SCFTs with (0, 2) supersymmetry in two dimensions and \( \mathcal{N} \) = 2 supersymmetry in one dimension. The geometry of Y2n+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 AdS3 × Y7 solution without knowing its explicit form. We interpret this as a geometric dual of c-extremization in (0, 2) SCFTs. For the case of AdS2 × Y9 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 AdS4. We also study many specific examples of the type AdS3 × T2 × Y5, 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 T2 of certain d = 4 quiver gauge theories associated with five-dimensional Sasaki-Einstein metrics and, surprisingly, come to a negative conclusion.

Keywords

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

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Institute for Theoretical Physics and Center for Extreme Matter and Emergent PhenomenaUtrecht UniversityUtrechtThe Netherlands
  2. 2.Blackett LaboratoryImperial CollegeLondonU.K.
  3. 3.Department of MathematicsKing’s College LondonLondonU.K.
  4. 4.Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory QuarterOxfordU.K.

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