A Cubic Deformation of ABJM: The Squashed, Stretched, Warped, and Perturbed Gets Invaded

TL;DR

This paper explores a cubic superpotential deformation of ABJM theory, leading to a new superconformal phase with a warped AdS4 solution, and analyzes the resulting KK graviton spectrum revealing complex supermultiplet structures.

Contribution

It provides a detailed numerical and analytical analysis of the graviton spectrum in a deformed ABJM setup, highlighting the space invaders phenomenon in KK spectra.

Findings

Complete graviton spectrum computed numerically

Analytical spectrum of short multiplets derived

Supermultiplet structure does not align KK level by level

Abstract

A superpotential deformation that is cubic in one of the chiral superfields of ABJM makes the latter theory flow into a new, ${\cal N}=2$ superconformal phase. This is holographically dual to a warped $\textrm{AdS}_4 \times_w S^7$ solution of M-theory equipped with a squashed and stretched metric on $S^7$. We determine the spectrum of spin-2 operators of the cubic deformation at low energies by computing the spectrum of Kaluza-Klein (KK) gravitons over the dual AdS$_4$ solution. We calculate, numerically, the complete graviton spectrum and, analytically, the spectrum of gravitons that belong to short multiplets. We also use group theory to assess the structure of the full KK spectrum, and conclude that ${\cal N}=2$ supermultiplets cannot be allocated KK level by KK level. This phenomenon, usually referred to as "space invaders scenario", is also known to occur for another $\textrm{AdS}_4$ solution based on a different squashed $S^7$.