The Squashed, Stretched, and Warped Gets Perturbed

TL;DR

This paper calculates the spectrum of spin-2 modes in a warped AdS_4 x squashed 7-sphere background, confirming duality with a specific N=2 superconformal Chern-Simons theory through spectrum analysis.

Contribution

It provides a detailed Kaluza-Klein reduction and matches the spin-2 spectrum with dual gauge theory operators, confirming the AdS/CFT correspondence for this background.

Findings

Spin-2 spectrum matches group theoretic predictions.

Mass-squared is quadratic in quantum numbers.

Most operators are in long multiplets with determined dimensions.

Abstract

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 x SU(3) symmetry, has been conjectured to be dual to a U(N) x U(N) N=2 superconformal Chern-Simons theory with a sextic superpotential. We find that the U(1)_R x 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.