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.
Highlights
One imposes the conditions for supersymmetry, i.e. the existence of Killing spinors, but relaxes the equation of motion of the five-form
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 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
Summary
One imposes the conditions for supersymmetry, i.e. the existence of Killing spinors, but relaxes the equation of motion of the five-form. To set up c-extremization it was necessary to impose an additional integral constraint on the supersymmetric geometries, whose precise form we will recall later The significance of this constraint, which is implied by the five-form equation of motion, is that it provides a sufficient condition in order to be able to consistently impose flux quantization of the five-form. Focusing on this class of supersymmetric geometries, the c-extremization begins with a complex cone C(Y7), with a holomorphic (4, 0)-form, and a holomorphic U(1)s action. Suppose we compactify this quiver gauge theory on a Riemann surface Σg with a “twist”, i.e. switching on background gauge fields associated with the
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