Toric geometry and the dual of I-extremization

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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



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