We consider 4d N=1 SCFTs, topologically twisted on compact constant curvature
Riemann surfaces, giving rise to 2d N=(0,2) SCFTs. The exact R-current of these
2d SCFT extremizes the central charge c_{2d}, similarly to the 4d picture,
where the exact R-current maximizes the central charge a_{4d}. 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 N=2 truncation of T^{1,1} with one Betti vector multiplet, dual
to the baryonic current on the CFT side. The holographic realization of the
flow across dimensions connects AdS_5 to AdS_3 vacua in the supergravity
picture. We verify the existence of the flow to AdS_3 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 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.Comment: 28 pages, 5 figures, typos fixed and additional explanations adde
