### Toric geometry and the dual of I-extremization

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1904.04282v2.pdf | Working paper | 1.31 MB | Adobe PDF | View/Open |

Title: | Toric geometry and the dual of I-extremization |

Authors: | Gauntlett, JP Martelli, D Sparks, J |

Item Type: | Working Paper |

Abstract: | We consider d=3, N=2 gauge theories arising on membranes sitting at the apex of an arbitrary toric Calabi-Yau 4-fold cone singularity that are then further compactified on a Riemann surface, Σg, with a topological twist that preserves two supersymmetries. If the theories flow to a superconformal quantum mechanics in the infrared, then they have a D=11 supergravity dual of the form AdS2×Y9, with electric four-form flux and where Y9 is topologically a fibration of a Sasakian Y7 over Σg. These D=11 solutions are also expected to arise as the near horizon limit of magnetically charged black holes in AdS4×Y7, with a Sasaki-Einstein metric on Y7. We show that an off-shell entropy function for the dual AdS2 solutions may be computed using the toric data and Kähler class parameters of the Calabi-Yau 4-fold, that are encoded in a master volume, as well as a set of integers that determine the fibration of Y7 over Σg and a Kähler class parameter for Σg. We also discuss the class of supersymmetric AdS3×Y7 solutions of type IIB supergravity with five-form flux only in the case that Y7 is toric, and show how the off-shell central charge of the dual field theory can be obtained from the toric data. We illustrate with several examples, finding agreement both with explicit supergravity solutions as well as with some known field theory results concerning I-extremization. |

Issue Date: | 28-Jun-2019 |

URI: | http://hdl.handle.net/10044/1/72631 |

Publisher: | arXiv |

Copyright Statement: | © 2019 The Authors. |

Sponsor/Funder: | Engineering & Physical Science Research Council (EPSRC) Commission of the European Communities Science and Technology Facilities Council (STFC) |

Funder's Grant Number: | EP/K034456/1 339140 ST/P000762/1 |

Keywords: | Science & Technology Physical Sciences Physics, Particles & Fields Physics AdS-CFT Correspondence Gauge-gravity correspondence Black Holes in String Theory Supersymmetric Gauge Theory SASAKI-EINSTEIN MANIFOLDS Science & Technology Physical Sciences Physics, Particles & Fields Physics AdS-CFT Correspondence Gauge-gravity correspondence Black Holes in String Theory Supersymmetric Gauge Theory SASAKI-EINSTEIN MANIFOLDS hep-th hep-th 01 Mathematical Sciences 02 Physical Sciences Nuclear & Particles Physics |

Publication Status: | Published |

Appears in Collections: | Physics Theoretical Physics |