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.

6 pages, 6 figures; v2: refs added, published version

References in corpus (9)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Notes on SUSY Gauge Theories on Three-Sphere
• Sasaki-Einstein Manifolds and Volume Minimisation
• Moduli spaces of Chern-Simons quiver gauge theories and AdS_4/CFT_3
• Brane Tilings and M2 Branes
• M2-branes on Orbifolds of the Cone over Q^{1,1,1}
• Towards M2-brane Theories for Generic Toric Singularities
• Phases of M2-brane Theories
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations