Betti multiplets, flows across dimensions and c-extremization

Abstract

We consider 4d mathcal{N} = 1 SCFTs, topologically twisted on compact constant curvature Riemann surfaces, giving rise to 2d mathcal{N} = (0, 2) SCFTs. The exact R-current of these 2d SCFT extremizes the central charge c2d, similarly to the 4d picture, where the exact R-current maximizes the central charge a4d. There are global currents that do not mix with the R-current in 4d but their mixing becomes non trivial in 2d. In this paper we study the holographic dual of this process by analyzing a 5d mathcal{N} = 2 truncation of T1,1 with one Betti vector multiplet, dual to the baryonic current on the CFT side. The holographic realization of the flow across dimensions connects AdS5 to AdS3 vacua in the supergravity picture. We verify the existence of the flow to AdS3 solutions and we retrieve the field theory results for the mixing of the Betti vector with the graviphoton. Moreover, we extract the central charge from the Brown-Henneaux formula, matching with the results obtained in field theory. We develop a general formalism to obtain the central charge of a 2d SCFT from 5d mathcal{N} = 2 gauged supergravity with a generic number of vector multiplets, showing that its extremization corresponds to an attractor mechanism for the scalars in the supergravity picture.