3D N=2 ADE^ Chern-Simons quivers

Abstract

We study 3d N = 2 Chern-Simons (CS) quiver theories on S 3 and Σ g × S 1 . Using localization results, we examine their partition functions in the large rank limit and requiring the resulting matrix models to be local, find a large class of quiver theories that include quivers in one-to-one correspondence with the ADE Dynkin diagrams. We compute explicitly the partition function on S 3 for D quivers and that on Σ g × S 1 for AD quivers, which lead to certain predictions for their holographic duals. We also provide a new and simple proof of the "index theorem", extending its applicability to a larger class of theories than considered before in the literature. * d.jain@saha.ac.in † augniva.ray@saha.ac.in ∆ (a,b) + ∆ (b,a) = 1 .(1.2)Note that for N ≥ 3 case, this condition is automatic since the supersymmetry enhancement fixes the R-charges to be 1 2 and ADE classification was presented in [14]. We will then explicitly solve the large N matrix model of the N = 2 D quiver theories 1 , whose dual geometry involves certain 7-dimensional Sasaki-Einstein manifolds Y 7 . Computation of their volumes directly does not necessarily give the volume for the Calabi-Yau (CY) metric necessary for

AdS black holes, holography and localization

“…50 For a large class of these theories the large N method discussed in Sect. 4.3 applies and the twisted index has been evaluated in Hosseini and Zaffaroni (2016), Hosseini and Mekareeya (2016), Jain and Ray (2019) and Jain (2019). Quite remarkably, in all these theories the on-shell twisted superpotential coincides with the corresponding S 3 free energy (Hosseini and…”

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).…”

Aspects of AdS2 classification in M-theory: solutions with mesonic and baryonic charges

“…For all these dual pairs the free energy of the field theory on S 3 was shown to agree with the regularized on-shell action on the gravity side largely using techniques presented in [33] (see also [34] for recent applications). More recently, the topologically twisted index of a number of these field theories has been computed [11,12,35,36]. Given the impressive match of the free energy on S 3 , it is natural to expect that the topologically twisted index in these cases would be related to the entropy of the dual magnetically charged asymptotically AdS 4 black holes.…”

“…Second, we require f 1 U (x 1 ) > 0 for a positive definite metric, which yields 35) where x ± are the zeros of U (x 1 ). Note that the solution has a finite volume only when c 2 1 > 4 3f 2 f 3 , so we assume this to be the case.…”