We use direct Kaluza-Klein reduction to calculate the spectrum of spin-2 modes around a warped product of AdS 4 and a certain squashed and stretched 7-sphere. The modes turn out to be polynomials in the four complex variables parameterizing the sphere, and their complex conjugates. The background, which possesses U(1) R × SU(3) symmetry, has been conjectured to be dual to a U(N) × U(N) = 2 superconformal Chern-Simons theory with a sextic superpotential. We find that the U(1) R × SU(3) quantum numbers of spin-2 modes are in agreement with those determined in arXiv:0809.3773 through a group theoretic method, and with the spectrum of spin-2 gauge invariant operators in the Chern-Simons gauge theory. The mass-squared in AdS 4 is found to be quadratic in these quantum numbers and the Kaluza-Klein excitation number. Most of the spin-2 operators belong to long multiplets, and we determine their dimensions via the AdS/CFT correspondence.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics
- AdS-CFT Correspondence
- Chern-Simons Theories
- Supergravity Models