Superconformal Chern-Simons theories from del Pezzo geometries

A bstract We present an explicit expression for the grand potential of the U( N ) 3 superconformal Chern-Simons theory with the Chern-Simons levels being ( k , 0, − k ). From the viewpoint of the Newton polygon, it is expected that the grand potential is given by the free energy of the topological string theory on the local D 5 del Pezzo geometry, though the explicit identification was a puzzle for years. We show how the expectation is realized explicitly. As a bonus, we can also study the ℤ 2 orbifold of this theory and find the grand potential is now given in terms of the local E 7 del Pezzo geometry.