Free Energy of b D n Quiver Chern-Simons Theories

We apply the matrix model of Kapustin, Willett and Yaakov to compute the free energy ofN = 3 Chern-Simons matter theories with b Dn quivers in the large N limit. We conjecture a general expression for the free energy that is explicitly invariant under Seiberg duality and show that it can be interpreted as a sum over certain graphs known as signed graphs. Through the AdS/CFT correspondence, this leads to a prediction for the volume of certain tri-Sasaki Einstein manifolds. We also study the unfolding procedure, which relates these b Dn quivers to b A2n 5 quivers. Furthermore, we consider the addition of massive fundamental flavor fields, verifying that integrating these out decreases the free energy in accordance with the F-theorem.