Proving the equivalence of $c$-extremization and its gravitational dual for all toric quivers

Abstract

The gravitational dual of $c$-extremization for a class of $(0,2)$ two-dimensional theories obtained by twisted compactifications of D3-brane gauge theories living at a toric Calabi-Yau three-fold has been recently proposed. The equivalence of this construction with $c$-extremization has been checked in various examples and holds also off-shell. In this note we prove that such equivalence holds for an arbitrary toric Calabi-Yau. We do it by generalizing the proof of the equivalence between $a$-maximization and volume minimization for four-dimensional toric quivers. By an explicit parameterization of the R-charges we map the trial right-moving central charge $c_r$ into the off-shell functional to be extremized in gravity. We also observe that the similar construction for M2-branes on ${\mathbb{C}}^4$ is equivalent to the $\mathcal{I}$-extremization principle that leads to the microscopic counting for the entropy of magnetically charged black holes in AdS${}_4\times S^7$. Also this equivalence holds off-shell.

arXiv comment35 pages

References in corpus (50)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• The Holographic Weyl anomaly
• Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity
• The Exact Superconformal R-Symmetry Maximizes a
• Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
• 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
• Brane Dimers and Quiver Gauge Theories
• A topologically twisted index for three-dimensional supersymmetric theories
• Sasaki-Einstein Manifolds and Volume Minimisation
• Einstein manifolds and conformal field theories
• The Geometric Dual of a-maximisation for Toric Sasaki-Einstein Manifolds
• New Einstein-Sasaki Spaces in Five and Higher Dimensions
• Dimer models and toric diagrams
• Four-Dimensional SCFTs from M5-Branes
• Toric Geometry, Sasaki-Einstein Manifolds and a New Infinite Class of AdS/CFT Duals
• Multi-Matrix Models and Tri-Sasaki Einstein Spaces
• Two-dimensional SCFTs from wrapped branes and c-extremization
• Baryons and Domain Walls in an N = 1 Superconformal Gauge Theory
• Supersymmetric AdS_4 black holes and attractors
• Exact two-dimensional superconformal R-symmetry and c-extremization
• Comments on twisted indices in 3d supersymmetric gauge theories
• From Sasaki-Einstein spaces to quivers via BPS geodesics: Lpqr
• Exact microstate counting for dyonic black holes in AdS4
• Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity
• The dual superconformal theory for Lpqr manifolds
• R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization
• Brane Tilings and M2 Branes
• Para-Liouville/Toda central charges from M5-branes
• Static supersymmetric black holes in AdS_4 with spherical symmetry
• A Universal Counting of Black Hole Microstates in AdS${}_4$
• Large $N$ matrix models for 3d $\mathcal{N}=2$ theories: twisted index, free energy and black holes
• Two-dimensional SCFTs from D3-branes
• Large $N$ topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces
• AdS/CFT Dual Pairs from M5-Branes on Riemann Surfaces
• Topologically twisted indices in five dimensions and holography
• Five-dimensional Supergravity Dual of a-Maximization
• Liouville/Toda central charges from M5-branes
• A geometric dual of $c$-extremization
• From Toric Geometry to Quiver Gauge Theory: the Equivalence of a-maximization and Z-minimization
• The Cardy limit of the topologically twisted index and black strings in AdS${}_5$
• F-theory and AdS_3/CFT_2 (2,0)
• Supergravity dual of c-extremization
• Toric geometry and the dual of $c$-extremization
• Comments on a-maximization from gauged supergravity
• Comments on Anomalies and Charges of Toric-Quiver Duals
• Betti multiplets, flows across dimensions and c-extremization
• Surveying 4d SCFTs twisted on Riemann surfaces
• c-extremization from toric geometry

Cited by in corpus (20)

• Accelerating Black Holes and Spinning Spindles
• Lectures on AdS Black Holes, Holography and Localization
• Rotating multi-charge spindles and their microstates
• Geometry of $\mathcal{I}$-extremization and black holes microstates
• Equivariant localization and holography
• Fibred GK geometry and supersymmetric $AdS$ solutions
• Entropy functions for accelerating black holes
• Black holes with baryonic charge and $\mathcal{I}$-extremization
• Microstates of rotating AdS${}_5$ strings
• Localization and Attraction
• Evidence for a 5d F-theorem
• Twisted $\mathcal{N}=1$ SCFTs and their AdS${}_3$ duals
• The joy of factorization at large $N$: five-dimensional indices and AdS black holes
• 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
• $N=(2,0)$ AdS${}_3$ Solutions of M-theory
• Uplifting dyonic AdS${}_4$ black holes on seven-dimensional Sasaki-Einstein manifolds
• $\mathcal{I}$-extremization with baryonic charges
• Constant maps in equivariant topological strings and geometric modeling of fluxes