## 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 Σ_{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 Σ_{g}. 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 language | English |
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Article number | 204 |

Number of pages | 50 |

Journal | Journal of High Energy Physics |

Volume | 2019 |

Issue number | 1 |

DOIs | |

Publication status | Published - 28 Jan 2019 |

## Keywords

- AdS-CFT Correspondence
- Supersymmetric Gauge Theory