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.

arXiv comment6 pages, 6 figures; v2: refs added, published version

References in corpus (29)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
• The Exact Superconformal R-Symmetry Extremizes Z
• From weak to strong coupling in ABJM theory
• Notes on SUSY Gauge Theories on Three-Sphere
• Sasaki-Einstein Manifolds and Volume Minimisation
• The Geometric Dual of a-maximisation for Toric Sasaki-Einstein Manifolds
• Multi-Matrix Models and Tri-Sasaki Einstein Spaces
• Tilings, Chern-Simons Theories and M2 Branes
• Moduli spaces of Chern-Simons quiver gauge theories and AdS_4/CFT_3
• Brane Tilings and M2 Branes
• Chiral flavors and M2-branes at toric CY4 singularities
• Notes on adding D6 branes wrapping RP3 in AdS4 x CP3
• The large N limit of quiver matrix models and Sasaki-Einstein manifolds
• M2-branes on Orbifolds of the Cone over Q^{1,1,1}
• Towards M2-brane Theories for Generic Toric Singularities
• Calculating the partition function of N=2 Gauge theories on $S^3$ and AdS/CFT correspondence
• From Necklace Quivers to the F-theorem, Operator Counting, and T(U(N))
• Quantum moduli space of Chern-Simons quivers, wrapped D6-branes and AdS4/CFT3
• Phases of M2-brane Theories
• Matrix Models for Supersymmetric Chern-Simons Theories with an ADE Classification
• The Large N Limit of Toric Chern-Simons Matter Theories and Their Duals
• Operator Counting and Eigenvalue Distributions for 3D Supersymmetric Gauge Theories
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
• Tests of AdS${}_4$/CFT${}_3$ correspondence for $\mathcal{N}=2$ chiral-like theory
• Z Extremization in Chiral-Like Chern Simons Theories
• Chern-Simons: Fano and Calabi-Yau
• Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter Fields