A geometric dual of $c$-extremization

Abstract

We consider supersymmetric AdS${}_3\times Y_7$ and AdS${}_2\times Y_9$ solutions of type IIB and $D=11$ supergravity, respectively, that are holographically dual to SCFTs with $(0,2)$ supersymmetry in two dimensions and $\mathcal{N}=2$ supersymmetry in one dimension. The geometry of $Y_{2n+1}$, which can be defined for $n\ge 3$, 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${}_3\times Y_7$ 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${}_2\times Y_9$ 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${}_3\times T^2\times Y_5$, 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.

arXiv comment67 pages. Minor changes, published version

References in corpus (58)

• Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity
• The Exact Superconformal R-Symmetry Maximizes a
• The Exact Superconformal R-Symmetry Extremizes Z
• On Flux Quantization In M-Theory And The Effective Action
• Eleven Dimensional Origin of String/String Duality: A One Loop Test
• Gauge Theories from Toric Geometry and Brane Tilings
• Black hole microstates in AdS${}_4$ from supersymmetric localization
• An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals
• A One-Loop Test Of String Duality
• A topologically twisted index for three-dimensional supersymmetric theories
• Sasaki-Einstein Manifolds and Volume Minimisation
• The Geometric Dual of a-maximisation for Toric Sasaki-Einstein Manifolds
• New Einstein-Sasaki Spaces in Five and Higher Dimensions
• Toric Geometry, Sasaki-Einstein Manifolds and a New Infinite Class of AdS/CFT Duals
• Two-dimensional SCFTs from wrapped branes and c-extremization
• Supersymmetry of Anti-de Sitter Black Holes
• Toric Sasaki-Einstein metrics on S^2 x S^3
• Consistent Kaluza-Klein Reductions for General Supersymmetric AdS Solutions
• Exact two-dimensional superconformal R-symmetry and c-extremization
• Comments on twisted indices in 3d supersymmetric gauge theories
• Supersymmetric AdS_5 Solutions of Type IIB Supergravity
• From Sasaki-Einstein spaces to quivers via BPS geodesics: Lpqr
• Exact microstate counting for dyonic black holes in AdS4
• Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index
• The dual superconformal theory for Lpqr manifolds
• R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization
• Central Charges and $U(1{)}_R$ Symmetries in $\mathcal{N}=1$ Super Yang-Mills
• AdS(3) Solutions of IIB Supergravity from D3-branes
• A Universal Counting of Black Hole Microstates in AdS${}_4$
• Supersymmetric AdS_3, AdS_2 and Bubble Solutions
• Large $N$ matrix models for 3d $\mathcal{N}=2$ theories: twisted index, free energy and black holes
• Supersymmetric gauge theories with decoupled operators and chiral ring stability
• Obstructions to the Existence of Sasaki-Einstein Metrics
• Sasaki-Einstein Metrics on S^2 x S^3
• Two-dimensional SCFTs from D3-branes
• Branes and Calibrated Geometries
• M-Theory on Spin(7) Manifolds
• A One-loop Test of Quantum Black Holes in Anti de Sitter Space
• Supersymmetric AdS_3 solutions of type IIB supergravity
• Comments on AdS2 solutions of D=11 Supergravity
• Microstate Counting of $Ad{S}_4$ Hyperbolic Black Hole Entropy via the Topologically Twisted Index
• Five-dimensional Supergravity Dual of a-Maximization
• A New Infinite Class of Quiver Gauge Theories
• New supersymmetric AdS_3 solutions
• From Toric Geometry to Quiver Gauge Theory: the Equivalence of a-maximization and Z-minimization
• F-theory and AdS_3/CFT_2 (2,0)
• AdS Solutions Through Transgression
• Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds
• Geometries with Killing Spinors and Supersymmetric AdS Solutions
• Resolutions of non-regular Ricci-flat Kahler cones
• Supergravity dual of c-extremization
• AdS_3 x S^3 x S^3 x S^1 Solutions of Type IIB String Theory
• Accidents in (0,2) Landau-Ginzburg theories
• N=1 Field Theories and Fluxes in IIB String Theory
• Sasakian Geometry, Hypersurface Singularities, and Einstein Metrics
• New Example of Infinite Family of Quiver Gauge Theories
• c-extremization from toric geometry
• Comments on AdS_2 Gravity

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• Accelerating Black Holes and Spinning Spindles
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• Lectures on AdS Black Holes, Holography and Localization
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• M5-branes wrapped on a spindle
• Surface Defect, Anomalies and $b$-Extremization
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• $\mathcal{N}=(2,2)$ AdS${}_3$ from D3-branes wrapped on Riemann surfaces
• M2-branes on Discs and Multi-Charged Spindles
• Equivariant localization and holography
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• ${\text{AdS}}_2\times {\text{S}}^2\times {\text{CY}}_2$ solutions in Type IIB with 8 supersymmetries
• Proving the equivalence of $c$-extremization and its gravitational dual for all toric quivers
• AdS${}_2$ duals to ADHM quivers with Wilson lines
• Fibred GK geometry and supersymmetric $AdS$ solutions
• Entropy functions for accelerating black holes
• Black holes with baryonic charge and $\mathcal{I}$-extremization
• AdS${}_3$ solutions with $\mathcal{N}=(3,0)$ from S${}^3\times$S${}^3$ fibrations
• Equivariant localization for AdS/CFT
• Microstates of rotating AdS${}_5$ strings
• Localization and Attraction
• Leigh-Strassler compactified on a spindle
• On AdS${}_3$ solutions of Type IIB
• Microstates of accelerating and supersymmetric AdS${}_4$ black holes from the spindle index
• New AdS${}_2$ supergravity duals of 4d SCFTs with defects
• Evidence for a 5d F-theorem
• Universal AdS black holes in theories with sixteen supercharges and their microstates
• Twisted $\mathcal{N}=1$ SCFTs and their AdS${}_3$ duals
• New AdS${}_2$ backgrounds and $\mathcal{N}=4$ Conformal Quantum Mechanics
• On Type IIA AdS${}_3$ solutions and massive GK geometries
• $\mathcal{I}$/$c$-Extremization in M/F-Duality
• The Near-Horizon Geometry of Supersymmetric Rotating AdS${}_4$ Black Holes in M-theory
• NUTs, Bolts, and Spindles
• $N=(2,0)$ AdS${}_3$ Solutions of M-theory
• Uplifting dyonic AdS${}_4$ black holes on seven-dimensional Sasaki-Einstein manifolds
• Branes wrapped on quadrilaterals
• $\mathcal{I}$-extremization with baryonic charges
• Constant maps in equivariant topological strings and geometric modeling of fluxes