Free energy of $ {{\widehat{D}}_n} $ quiver Chern-Simons theories

Abstract

We apply the matrix model of Kapustin, Willett and Yaakov to compute the free energy of N = 3 Chern-Simons matter theories with D n 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 D n quivers to A 2n−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.

Sphere correlation functions and Verma modules

“…The N 3 2 behavior of the S 3 partition function was firstly discovered in [26] for ABJM model whose M-theory dual is AdS 4 × S 7 /Z k . It also shows up in a large class of 3d N = 3 [27][28][29][30] and N = 2 [31][32][33][34][35][36][37][38][39] Chern-Simons matter theories whose M-theory duals are AdS 4 × Y 7 where Y 7 are Sasaki-Einstein manifolds in such a way that the S 3 free energy is proportional to N with the coefficient depending on the volume of Y 7 . It would be interesting to give an holographic interpretation for our formula, perhaps by turning on the analogues of ζ and m on the supergravity side to study the dual to Z(m; ζ).…”

New 3d $$ \mathcal{N} $$ = 2 SCFT’s with N3/2 scaling

“…We will see that the presence of adjoint matter fields requires a modification of the algorithm of [15,18], which will play an important role in our analysis. 3…”

“…In the following we will show the general algorithm for solving the matrix model. In the case with equal ranks it reduces to the one of [11]; if the nodes have different ranks but no adjoint matter fields are present, it can be shown to coincide with the one of [15,18,26].…”

“…We show that the free energy of such models scales as N 3/2 and we provide an algorithm to compute it in the presence of extra adjoint fields. This algorithm generalizes the one of [15,18], where it was first noticed that a split in the eigenvalues of the matrix model is induced by the varying ranks of the gauge groups. We will show that in presence of charged adjoint matter the prescription of [15,18] requires some modifications.…”

Partition functions of superconformal Chern-Simons theories from Fermi gas approach

“…earlier works [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]. Especially it is worthwhile to mention that, according to [15] the expression of the coefficient C was given a geometrical interpretation as the classical volume inside the Fermi surface.…”