Large-$N$ Free Energy of Chiral $\mathcal{N}=2$ Chern-Simons-Matter Theories

Abstract

We present the first successful large-$N$ computation of the $S^3$ free energy in chiral $\mathcal{N}=2$ Chern-Simons-matter theories, long believed to evade the universal M2-brane scaling $F_{S^3}\!\sim\!N^{3/2}$. Using a stable numerical continuation method that directly solves the saddle-point equations, we obtain convergent large-$N$ solutions for benchmark chiral quivers, including the holographic dual to AdS$_4\times Q^{1,1,1}/\mathbb{Z}_k$ and $D_3$ models. The resulting free energies precisely match the holographic predictions, resolving a decade-old puzzle in AdS$_4$/CFT$_3$ and establishing a practical numerical framework for precision holography in strongly coupled gauge theories.