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 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 , 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.
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ArXiv ePrint: 1812.05597
On leave at the Galileo Galilei Institute, Largo Enrico Fermi, 2, 50125 Firenze, Italy. (Dario Martelli)
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Gauntlett, J.P., Martelli, D. & Sparks, J. Toric geometry and the dual of c-extremization. J. High Energ. Phys. 2019, 204 (2019). https://doi.org/10.1007/JHEP01(2019)204
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DOI: https://doi.org/10.1007/JHEP01(2019)204