Large-N limit of chiral quiver theories: free energy, supersymmetric indices and operator counting

We find the first analytic solution to the large-N saddle point equations for the S³ free energy of a chiral N=2 Chern-Simons-matter theory with an M-theory dual. Focusing on the chiral quiver dual to AdS₄× Q1,1,1/ Zₖ, we show how the long-range forces of the matrix model cancel at large N, resolving a long-standing tension with the expected N3/2 scaling. The resulting free energy precisely matches the holographic prediction for all assignments of trial R-charges. Our results extend to the superconformal and topologically twisted indices on S²× S¹, whose large-N and Cardy limit is determined by the same saddle. The solution agrees with the predictions of the operator counting method, giving strong evidence for this conjecture beyond non-chiral quivers. We support the analytic solution with a finite-N numerical analysis for multiple assignments of R-charges, extending recent numerical results obtained for this quiver.