A cubic deformation of ABJM: the squashed, stretched, warped, and perturbed gets invaded

Abstract

A superpotential deformation that is cubic in one of the chiral superfields of ABJM makes the latter theory flow into a new $$ \mathcal{N} $$ N = 2 superconformal phase. This is holographically dual to a warped AdS4×wS7 solution of M-theory equipped with a squashed and stretched metric on S7. 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 AdS4 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 $$ \mathcal{N} $$ 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 AdS4 solution based on a different squashed S7.

Global properties of the conformal manifold for S-fold backgrounds

“…At the special values χ = πm T , m ∈ Z, two vectors in the full KK spectrum, but outside the supergravity truncation, become massless, thus enhancing U(1) 2 to SU(2) × U(1) . This corresponds to a space invaders scenario [40,41]. Moreover, for vacua related by the shift χ → χ + 2π T , the entire Kaluza-Klein spectrum is identical, although differently distributed over the S 1 × S 5 KK levels along the lines described in [42], 3 while for χ = π T , the Kaluza-Klein spectrum differs.…”

“…which vanish for n = p. These correspond to the two gauge vectors at level n > 0 which become massless for these values of χ and enhance the U( 1), seen at S 1 KK level n = 0, back to SU(2). This is a bosonic version of the space invaders scenario [40,41], where higher Kaluza-Klein modes become massless.…”

Super-Chern-Simons spectra from exceptional field theory

“…These cubic terms can again be added to the superpotential to generate deformations that have direct analogues in four-dimensional N = 4 super-Yang Mills and ABJM. In the ABJM case, this cubic superpotential deformation is relevant [69,76] (see also [57]) and generates RG flow. In the present massive type IIA case, the cubic deformation is instead classically marginal according to tables 2, 4 and 7.…”

Kaluza-Klein fermion mass matrices from exceptional field theory and $$ \mathcal{N} $$ = 1 spectra

“…on AdS exist which are block-diagonal KK level by KK level. The consistent truncation requirement is critical for this block-diagonal structure, as the latter is absent for AdS solutions which do not uplift from a maximally supersymmetric lower-dimensional gauged supergravity [18,24]. The infinite-dimensional mass matrices for the KK bosonic perturbations above the relevant class of AdS solutions have been determined from ExFT in [13,14].…”