Abstract
We give a master formula for the spin-2 spectrum of a class of three-dimensional Chern-Simons theories at large N , with flavour group containing SU(3), that arise as infrared fixed points of the D2-brane worldvolume field theory and have AdS4 duals in massive type IIA supergravity. We use this formula to compute the spin-2 spectrum of the individual theories, discuss its supermultiplet structure and, for an mathcal{N} = 2 theory in this class, the spectrum of protected operators with spin 2. We also show that the trace of the Kaluza-Klein graviton mass matrix on the dual AdS4 solutions enjoys certain universality properties. These are shown to relate the class of AdS4 massive IIA solutions under consideration to a similar class of AdS4 solutions of D = 11 supergravity with the same symmetries. Finally, for the mathcal{N} = 2 AdS4 solution in this class, we study the entire spectrum at lowest Kaluza-Klein level and relate it to an analogue solution in D = 11 supergravity.
Highlights
Background geometryWe are interested in (Einstein frame) type IIA geometries of the form ds210 = e2A(y) gμν (x) + hμν (x, y) dxμdxν + ds26(y), (2.1)where (x, y) collectively denote the external and internal coordinates, respectively
We give a master formula for the spin-2 spectrum of a class of three-dimensional Chern-Simons theories at large N, with flavour group containing SU(3), that arise as infrared fixed points of the D2-brane worldvolume field theory and have AdS4 duals in massive type IIA supergravity
The first question is whether the universality of the n = 0 KK mass spectrum is lost at higher, n > 0 KK levels. Intuition dictates that this should be the case — a full KK spectroscopy analysis should be able to tell these compactifications apart. We address this question for the CPW AdS4 solution [5] of D = 11 supergravity and the massive type IIA AdS4 solution of [7]
Summary
A quick inspection of the eigenvalues (2.28) and (2.31) makes it obvious that these two series correspond to one and only branch of KK graviton masses. Directions transverse to the D2-branes, subject to the S6 constraint δIJ μI μJ = 1 These μI can be written in terms of the μi defined above (2.16) and the angle α as. The generic spectrum comes in the representations of SU(3) × U(1) that result from branching the symmetric traceless representation [n, 0, 0] of SO(7) for each n through SO(6) ∼ SU(4) and through (2.16), that is, n nl [n, 0, 0] S−U→(4). This follows from the most general expression, (A.11), that the mass operator of this class of geometries may have. The eigenfunctions (2.38) are polynomials in za, za, sin α, cos α
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