Toric geometry and the dual of c-extremization

Author: 

Gauntlett, G
Martelli, D
Sparks, J

Publication Date: 

28 January 2019

Journal: 

Journal of High Energy Physics

Last Updated: 

2020-04-03T14:58:05.477+01:00

Issue: 

1

Volume: 

2019

DOI: 

10.1007/JHEP01(2019)204

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 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.

Symplectic id: 

965429

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article