Toric geometry and the dual of c-extremization

Jerome P. Gauntlett*, Dario Martelli, James Sparks

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)
119 Downloads (Pure)


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 [InlineMediaObject not available: see fulltext.], 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.

Original languageEnglish
Article number204
Number of pages50
JournalJournal of High Energy Physics
Issue number1
Publication statusPublished - 28 Jan 2019


  • AdS-CFT Correspondence
  • Supersymmetric Gauge Theory


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