Toric geometry and the dual of c-extremization

Journal article

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 Y p,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 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.

Authors: Gauntlett, G; Martelli, D; Sparks, J

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer Berlin Heidelberg
• Journal: Journal of High Energy Physics
• Volume: 2019
• Issue: 1
• Article number: 204
• Publication date: 2019-01-28
• Acceptance date: 2019-01-19
• DOI: 10.1007/JHEP01(2019)204
• EISSN: 1029-8479
• ISSN: 1126-6708
• Keywords: AdS-CFT correspondence; supersymmetric gauge theory