Journal of High Energy Physics

, 2019:204 | Cite as

Toric geometry and the dual of c-extremization

  • Jerome P. GauntlettEmail author
  • Dario Martelli
  • James Sparks
Open Access
Regular Article - Theoretical Physics


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 Σg, 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 AdS3 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 Yp,q and Xp,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 Σg. We furthermore conjecture that the trial central charge Open image in new window , 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.


AdS-CFT Correspondence Supersymmetric Gauge Theory 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Jerome P. Gauntlett
    • 1
    Email author
  • Dario Martelli
    • 2
  • James Sparks
    • 3
  1. 1.Blackett LaboratoryImperial CollegeLondonU.K.
  2. 2.Department of MathematicsKing’s College LondonLondonU.K.
  3. 3.Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory QuarterOxfordU.K.

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