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

Abstract

We construct several novel examples of 3d N = 2 models whose free energy scales as N 3/2 at large N . This is the first step towards the identification of field theories with an M-theory dual. Furthermore, we match the volumes extracted from the free energy with the ones computed from the Hilbert series. We perform a similar analysis for the 4d N = 1 parents of the 3d models, matching the volume extracted from the a central charge to that obtained from the Hilbert series. For some of the 4d models, we show the existence of a Sasaki-Einstein metric on the internal space of the candidate type IIB gravity dual.

Microscopic entropy of rotating electrically charged AdS4 black holes from field theory localization

“…At the technical level, adding magnetic charges or electric charges and angular momentum simply changes an overall factor in the same matrix model. An attack on this question can probably be mounted following direct computations of indices and partition functions such as [70][71][72]. A rigorous understanding of these universal relations can possibly be achieved from the insightful work [73] and the formula therein Z Mq,p with an additional refinement.…”

Geometry of $$ \mathcal{I} $$-extremization and black holes microstates

“…The same analysis can be applied to other Sasaki-Einsten manifolds Y 7 without fivecycles. In particular, it applies to some of the models recently discussed in [10]. We can also provide a very general argument that applies to many different theories and it is based on very few assumptions.…”

“…The gravity dual of F -maximization is the volume minimization principle discovered in [2,3]. The equivalence of the two extremization principles has been checked in many examples [4][5][6][7][8][9][10], although there is no general proof, since the large N limit of the S 3 free energy is currently available only for a restricted class of theories.…”

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).…”