Rings of short N=3 superfields in three dimensions and M-theory on AdS_4 x N^{0,1,0}

TL;DR

This paper explores three-dimensional N=3 superconformal gauge theories, establishing a superfield ring structure, and identifies their dual M-theory backgrounds on AdS_4 x N^{0,1,0}, confirming the AdS/CFT correspondence through spectrum analysis.

Contribution

It introduces a superfield ring structure for N=3 theories and connects it to M-theory on AdS_4 x N^{0,1,0}, providing new insights into dualities and operator organization.

Findings

Derived shortening conditions for Osp(3|4) superalgebra.

Established the superfield ring structure generalizing N=2 chiral rings.

Matched the supergravity spectrum with the dual N=3 gauge theory operators.

Abstract

In this paper we investigate three-dimensional superconformal gauge theories with N=3 supersymmetry. Independently from specific models, we derive the shortening conditions for unitary representations of the Osp(3|4) superalgebra and we express them in terms of differential constraints on three dimensional N=3 superfields. We find a ring structure underlying these short representations, which is just the direct generalization of the chiral ring structure of N=2 theories. When the superconformal field theory is realized on the world-volume of an M2-brane such superfield ring is the counterpart of the ring defined by the algebraic geometry of the 8-dimensional cone transverse to the brane. This and other arguments identify the N=3 superconformal field theory dual to M-theory compactified on AdS_4 x N^{0,1,0}. It is an N=3 gauge theory with SU(N) x SU(N) gauge group coupled to a suitable set of hypermultiplets, with an additional Chern Simons interaction. The AdS/CFT correspondence can be directly verified using the recently worked out Kaluza Klein spectrum of N^{0,1,0} and we find a perfect match. We also note that besides the usual set of BPS conformal operators dual to the lightest KK states, we find that the composite operators corresponding to certain massive KK modes are organized into a massive spin 3/2 N=3 multiplet that might be identified with the super-Higgs multiplet of a spontaneously broken N=4 theory. We investigate this intriguing and inspiring feature in a separate paper.