Superconformal Chern-Simons Theories and the Squashed Seven Sphere

TL;DR

This paper explores supersymmetric completions of a 3D Chern-Simons theory with gauge group U(N)xU(N), identifying a known N=6 superconformal theory and proposing a new N=1 superconformal dual related to M-theory on a squashed seven-sphere.

Contribution

The paper identifies a new N=1 superconformal Chern-Simons theory with specific matter content and conjectures its duality to M-theory on a squashed seven-sphere background.

Findings

Confirmed the N=6 superconformal theory as a completion.

Proposed a new N=1 superconformal theory with specific matter fields.

Conjectured duality between the N=1 theory and M-theory on AdS_4 x Squashed S^7/Z_k.

Abstract

We show that there are two supersymmetric completions of the three-dimensional Chern-Simons theory of level k with gauge group U(N)xU(N) coupled to four sets of massless scalars and spinors in the bi-fundamental representation, if we require Sp(2) global symmetry with the matter fields in the fundamental representation of SU(4). One is the N=6 superconformal theory recently studied in arXiv:0806.1218 [hep-th] and another is a new theory with N=1 superconformal symmetry. We conjecture that the N=1 theory is dual to M theory on AdS_4 x Squashed S^7/Z_k.