Deformed $\mathcal{N}=8$ mechanics of $(8,8,0)$ multiplets

Abstract

We construct new models of `curved' SU$(4|1)$ supersymmetric mechanics based on two versions of the off-shell multiplet $(8,8,0)$ which are `mirror' to each other. The worldline realizations of the supergroup SU$(4|1)$ are treated as a deformation of flat $\mathcal{N}=8$, $d=1$ supersymmetry. Using SU$(4|1)$ chiral superfields, we derive invariant actions for the first-type $(8,8,0)$ multiplet, which parametrizes special Kähler manifolds. Since we are not aware of a manifestly SU$(4|1)$ covariant superfield formalism for the second-type $(8,8,0)$ multiplet, we perform a general construction of SU$(4|1)$ invariant actions for both multiplet types in terms of SU$(2|1)$ superfields. An important class of such actions enjoys superconformal OSp$(8|2)$ invariance. We also build off-shell actions for the SU$(4|1)$ multiplets $(6,8,2)$ and $(7,8,1)$ through appropriate substitutions for the component fields in the $(8,8,0)$ actions. The $(6,8,2)$ actions are shown to respect superconformal SU$(4|1,1)$ invariance.

1+34 pages; v2: section 3 revised, typos corrected, 5 additional references, clarifying comments and acknowledgment added, matches published version

References in corpus (7)

• Hierarchy of N=8 Mechanics Models
• Critical scaling dimension of D-module representations of N=4,7,8 Superconformal Algebras and constraints on Superconformal Mechanics
• Quantum SU(2$|$1) supersymmetric Calogero-Moser spinning systems
• Gauged spinning models with deformed supersymmetry
• SU(2|2) supersymmetric mechanics
• The quasi-nonassociative exceptional $F(4)$ deformed quantum oscillator
• Deformed supersymmetric quantum mechanics with spin variables

Cited by in corpus (5)

• ${\mathbb{CP}}^N$-Rosochatius system, superintegrability, supersymmetry
• Symmetries of deformed supersymmetric mechanics on Kähler manifolds
• A three-dimensional superconformal quantum mechanics with $sl(2|1)$ dynamical symmetry
• Supersymmetric Calogero models from superfield gauging
• Weak supersymmetric $su(N|1)$ quantum systems