Mass spectrum in AdS$_4\times U(1)\setminus U(3)/U(1) $ compactification using harmonic analysis

TL;DR

This paper computes the Kaluza-Klein mass spectrum of certain fields in an AdS$_4$ compactification of 11-dimensional supergravity on a specific 7-dimensional manifold, aiding understanding of dual 3D Chern-Simons theories.

Contribution

It provides the explicit mass spectrum for 0-form and 1-form fields in a novel AdS$_4$ compactification with a specific internal manifold.

Findings

Mass spectrum for 0-form fields derived.

Mass spectrum for 1-form fields derived.

Results support the gravity duals of 3D quiver Chern-Simons theories.

Abstract

In this paper we present the Kaluza-Klein mass spectrum of 0-form and 1-form fields that appear in AdS$_4\times B_7$ compactification of $d=11$ supergravity, where, $B_7=U(1)\setminus U(3)/ U(1)$. This theory belongs to the class of gravity duals to three dimensional quiver Chern-Simons matter theories as demonstrated by D.L Jafferis and A. Tomasiello in \cite{jaff}