Spectrum universality properties of holographic Chern-Simons theories

TL;DR

This paper derives a universal formula for the spin-2 spectrum of certain 3D Chern-Simons theories with AdS$_4$ duals, revealing spectral properties and universality relations across different supergravity solutions.

Contribution

It provides a master formula for the spin-2 spectrum of large N Chern-Simons theories with AdS$_4$ duals and uncovers universality properties linking different supergravity backgrounds.

Findings

Derived a master formula for the spin-2 spectrum.

Identified universality properties of the Kaluza-Klein graviton mass matrix.

Connected spectra of IIA and D=11 supergravity solutions.

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 AdS$_4$ 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 ${\cal N}=2$ 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 AdS$_4$ solutions enjoys certain universality properties. These are shown to relate the class of AdS$_4$ massive IIA solutions under consideration to a similar class of AdS$_4$ solutions of $D=11$ supergravity with the same symmetries. Finally, for the ${\cal N}=2$ AdS$_4$ 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.