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Exact results for 5d SCFTs of long quiver type

Exact results are derived for 5d SCFTs with holographic duals in Type IIB supergravity. These theories have relevant deformations that flow to linear quiver gauge theories, with the number of nodes large in the large-$N$ limits described by supergravity. Starting from a suitable formulation of the matrix models resulting from supersymmetric localization of the squashed $S^5$ partition functions, the saddle point equations are solved for generic quivers with $N_f=2N$ at all interior nodes, which includes the $T_N$ theories, and for a sample of theories with $N_f\neq 2N$ nodes including theories with Chern-Simons terms. The resulting exact expressions for the free energies and conformal central charges are consistent with supergravity predictions and, where available, with previous numerical field theory analyses.