AdS_4/CFT_3 -- Squashed, Stretched and Warped

TL;DR

This paper analyzes the spectrum of a specific M-theory background with N=2 supersymmetry, matching it with a dual superconformal Chern-Simons theory, and proposes a form for monopole operators in the U(2)xU(2) case.

Contribution

It computes the spectrum of short multiplets in a warped AdS_4 background and proposes a form for monopole operators in the dual gauge theory.

Findings

Spectrum matches gauge invariant operators in the dual theory.

Proposed monopole operators exhibit desired symmetry properties.

Enhanced symmetry for U(2)xU(2) at specific levels.

Abstract

We use group theoretic methods to calculate the spectrum of short multiplets around the extremum of N=8 gauged supergravity potential which possesses N=2 supersymmetry and SU(3) global symmetry. Upon uplifting to M-theory, it describes a warped product of AdS_4 and a certain squashed and stretched 7-sphere. We find quantum numbers in agreement with those of the gauge invariant operators in the N=2 superconformal Chern-Simons theory recently proposed to be the dual of this M-theory background. This theory is obtained from the U(N)xU(N) theory through deforming the superpotential by a term quadratic in one of the superfields. To construct this model explicitly, one needs to employ monopole operators whose complete understanding is still lacking. However, for the U(2)xU(2) gauge theory we make a proposal for the form of the monopole operators which has a number of desired properties. In particular, this proposal implies enhanced symmetry of the U(2)xU(2) ABJM theory for k=1,2; it makes its similarity to and subtle difference from the BLG theory quite explicit.