Geometric free energy of toric AdS4/CFT3 models

Understand

We study the supersymmetric free energy of three dimensional Chern-Simons-matter theories holographically dual to AdS$_4$ times toric Sasaki-Einstein seven-manifolds.

• In the large $N$ limit, we argue that the square of the free energy can be written as a quartic polynomial of trial R-charges.
• The coefficients of the polynomial are determined geometrically from the toric diagrams.
• We present the coefficients of the quartic polynomial explicitly for generic toric diagrams with up to 6 vertices, and some particular diagrams with 8 vertices.