Toric geometry and the dual of $c$-extremization

Abstract

We consider D3-brane gauge theories at an arbitrary toric Calabi-Yau 3-fold cone singularity that are then further compactified on a Riemann surface ${\Sigma }_g$, with an arbitrary partial topological twist for the global $U(1)$ symmetries. This constitutes a rich, infinite class of two-dimensional $(0,2)$ theories. Under the assumption that such a theory flows to a SCFT, we show that the supergravity formulas for the central charge and $R$-charges of BPS baryonic operators of the dual AdS${}_3$ solution may be computed using only the toric data of the Calabi-Yau 3-fold and the topological twist parameters. We exemplify the procedure for both the $Y^{p,q}$ and $X^{p,q}$ 3-fold singularities, along with their associated dual quiver gauge theories, showing that the new supergravity results perfectly match the field theory results obtained using $c$-extremization, for arbitrary twist over ${\Sigma }_g$. We furthermore conjecture that the trial central charge $\mathcal{Z}$, which we define in gravity, matches the field theory trial $c$-function off-shell, and show this holds in non-trivial examples. Finally, we check our general geometric formulae against a number of explicitly known supergravity solutions.

arXiv comment62 pages. Typos corrected, published version

References in corpus (25)

• Supergravity description of field theories on curved manifolds and a no go theorem
• The Exact Superconformal R-Symmetry Maximizes a
• Gauge Theories from Toric Geometry and Brane Tilings
• An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals
• Sasaki-Einstein Manifolds and Volume Minimisation
• The Geometric Dual of a-maximisation for Toric Sasaki-Einstein Manifolds
• Toric Geometry, Sasaki-Einstein Manifolds and a New Infinite Class of AdS/CFT Duals
• Two-dimensional SCFTs from wrapped branes and c-extremization
• Exact two-dimensional superconformal R-symmetry and c-extremization
• The Master Space of N=1 Gauge Theories
• R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization
• 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
• Obstructions to the Existence of Sasaki-Einstein Metrics
• Notes on toric Sasaki-Einstein seven-manifolds and AdS_4/CFT_3
• Two-dimensional SCFTs from D3-branes
• Magnetic and electric AdS solutions in string- and M-theory
• Supersymmetric AdS_3 solutions of type IIB supergravity
• F-theory and AdS_3/CFT_2 (2,0)
• AdS Solutions Through Transgression
• Geometries with Killing Spinors and Supersymmetric AdS Solutions
• Comments on Anomalies and Charges of Toric-Quiver Duals
• A Comprehensive Survey of Brane Tilings
• c-extremization from toric geometry

Cited by in corpus (25)

• Accelerating Black Holes and Spinning Spindles
• The BPS limit of rotating AdS black hole thermodynamics
• Lectures on AdS Black Holes, Holography and Localization
• Supersymmetric spindles
• Geometry of $\mathcal{I}$-extremization and black holes microstates
• Equivariant localization and holography
• Searching for surface defect CFTs within AdS${}_3$
• Proving the equivalence of $c$-extremization and its gravitational dual for all toric quivers
• ${\text{AdS}}_2\times {\text{S}}^2\times {\text{CY}}_2$ solutions in Type IIB with 8 supersymmetries
• AdS${}_2$ duals to ADHM quivers with Wilson lines
• Fibred GK geometry and supersymmetric $AdS$ solutions
• Black holes with baryonic charge and $\mathcal{I}$-extremization
• Microstates of rotating AdS${}_5$ strings
• Localization and Attraction
• On AdS${}_3$ solutions of Type IIB
• Evidence for a 5d F-theorem
• Twisted $\mathcal{N}=1$ SCFTs and their AdS${}_3$ duals
• 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
• Giant Gravitons and Volume Minimisation