A cubic deformation of ABJM: the squashed, stretched, warped, and perturbed gets invaded
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Springer
Received: July 23, 2020 Accepted: September 9, 2020 Published: October 7, 2020
Mattia Ces` aro,a Gabriel Lariosa and Oscar Varelaa,b a
Departamento de F´ısica Te´ orica and Instituto de F´ısica Te´ orica UAM/CSIC, Universidad Aut´ onoma de Madrid, Cantoblanco, 28049 Madrid, Spain b Department of Physics, Utah State University, Logan, UT 84322, U.S.A.
E-mail: [email protected], [email protected], [email protected] Abstract: A superpotential deformation that is cubic in one of the chiral superfields of ABJM makes the latter theory flow into a new N = 2 superconformal phase. This is holographically dual to a warped AdS4 ×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 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 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 AdS 4 solution based on a different squashed S 7 . Keywords: Gauge-gravity correspondence, Supergravity Models, M-Theory ArXiv ePrint: 2007.05172
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)041
JHEP10(2020)041
A cubic deformation of ABJM: the squashed, stretched, warped, and perturbed gets invaded
Contents 1
2 A cubic superpotential deformation of N = 8 ABJM 2.1 Field theory side 2.2 Gravity side
3 3 5
3 Spectrum of massive gravitons on the GMPS solution 3.1 Boundary value problem 3.2 Numerics 3.3 The complete numerical KK graviton spectrum 3.4 Analytic results: short and shadow gravitons 3.5 GMPS is not isometrically embedded in R8
8 9 10 13 14 18
4 Space invaders scenario
20
A Embedding SU(3)×U(1)p into SO(8)
22
B Possible space invasion patterns B.1 Space invaders at level n drawn from level n + 1 B.2 Matching the CPW short multiplets
25 25 29
1
Introduction
It is an interesting problem to characterise the low-energy physics that relevant deformations of superconformal field theories (SCFTs) will lead to. Focusing, for definiteness, on the Aharony-Bergman-Jafferis-Maldacena (ABJM) [1] SCFT defined on a stack of M2branes, there is a well-known relevant, mass deformation that makes the theory flow into a new infrared (IR) fixed point [2]. This deformation can be implemented at the level of the holomorphic superpotential by writing a new term, (Z 4 )2 , quadratic in one of the four chiral matter superfields, Z I , I = 1, . . . , 4, that the N = 2 formulation of ABJM encompasses. Both the resulting renormalisation group (RG) flow and its IR endpoint are manifestly N = 2 and preserve an SU(3) flavour group. The IR SCFT is holographically dual to an M-theory solution written by Co
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