AdS_4/CFT_3 -- Squashed, Stretched and Warped

TL;DR

The paper establishes a controlled AdS$_4$/CFT$_3$ duality for a warped M-theory background with a squashed and stretched $S^7$ by performing a group-theoretic KK analysis around an $ ext{SU}(3) imes ext{U}(1)_R$-invariant extremum of the $ ext{N}=8$ gauged supergravity potential and organizing the result into $ ext{N}=2$ multiplets. It then constructs and analyzes the IR gauge theory dual as a deformed ABJM theory at $k=1,2$, using monopole operators to realize $ ext{SU}(4)$ invariance and to generate the correct operator spectrum; a quadratic deformation is shown to flow to an IR fixed point with sextic interactions compatible with the gravity side. A central outcome is that only the Scenario I embedding of $ ext{SU}(3) imes ext{U}(1)_R$ into $ ext{SO}(8)$ yields a KK spectrum matching the gauge theory operators, reinforcing the proposed duality and highlighting the essential role of monopole operators in the $ ext{U}(2) imes ext{U}(2)$ ABJM theory. The results illuminate parity breaking and the detailed mapping between supergravity short multiplets and CFT operators, advancing explicit AdS$_4$/CFT$_3$ correspondences for nontrivial internal geometries.

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.