Gauging N=4 Supersymmetric Mechanics

Abstract

We argue that off-shell dualities between d=1 supermultiplets with different sets of physical bosonic components and the same number of fermionic ones are related to gauging some symmetries in the actions of the supermultiplets with maximal sets of physical bosons. Our gauging procedure uses off-shell superfields and so is manifestly supersymmetric. We focus on N=4 supersymmetric mechanics and show that various actions of the multiplet (3,4,1) amount to some gauge choices in the gauged superfield actions of the linear or nonlinear (4,4,0) multiplets. In particular, the conformally invariant (3,4,1) superpotential is generated by the Fayet-Iliopoulos term of the gauge superfield. We find a new nonlinear variant of the multiplet (4,4,0), such that its simplest superfield action produces the most general 4-dim hyper-Kähler metric with one triholomorphic isometry as the bosonic target metric. We also elaborate on some other instructive examples of N=4 superfield gaugings, including a non-abelian gauging which relates the free linear (4,4,0) multiplet to a self-interacting (1,4,3) multiplet.

32 pages, minor amendments in Sect. 2, version to appear in Nucl. Phys. B

References in corpus (9)

• ABC of N=8, d=1 supermultiplets
• Classification of irreps and invariants of the N-extended Supersymmetric Quantum Mechanics
• "Root" Action for N=4 Supersymmetric Mechanics Theories
• When Superspace Is Not Enough
• The Quantum Mechanics SUSY Algebra: An Introductory Review
• N=8 Mechanics in SU(2)xSU(2) Harmonic Superspace
• N=4, d=1 tensor multiplet and hyper-Kahler sigma-models
• A Journey Through Garden Algebras
• N=4 supersymmetric Eguchi-Hanson sigma model in d=1

Cited by in corpus (59)

• Supersymmetric Calogero models by gauging
• Superconformal mechanics
• Hierarchy of N=8 Mechanics Models
• New D(2,1;alpha) Mechanics with Spin Variables
• N = 4 mechanics of general (4, 4, 0) multiplets
• Gauging N=4 supersymmetric mechanics II: (1,4,3) models from the (4,4,0) ones
• 4D, N = 1 Supersymmetry Genomics (I)
• Deformed Supersymmetric Mechanics
• SQM with Non-Abelian Self-Dual Fields: Harmonic Superspace Description
• Gauge Fields, Nonlinear Realizations, Supersymmetry
• New Model of N=8 Superconformal Mechanics
• Biharmonic Superspace for N=4 Mechanics
• Second Hopf map and supersymmetric mechanics with Yang monopole
• Superconformal mechanics in SU(2|1) superspace
• Supersymmetric hyperbolic Calogero-Sutherland models by gauging
• The Common Origin of Linear and Nonlinear Chiral Multiplets in N=4 Mechanics
• SU(2) reduction in N=4 supersymmetric mechanics
• On non-minimal N=4 supermultiplets in 1D and their associated sigma-models
• SU(2|2) supersymmetric mechanics
• Gauged spinning models with deformed supersymmetry
• N=4, 3D Supersymmetric Quantum Mechanics in Non-Abelian Monopole Background
• N=4 superconformal mechanics from the su(2) perspective
• Massive quiver matrix models for massive charged particles in AdS
• SU(2|1) mechanics and harmonic superspace
• Geometry of N=4, d=1 nonlinear supermultiplet
• Superfield Formulation of Nonlinear N=4 Supermultiplets
• Nonlinear (4, 8, 4) Multiplet of N=8, d=1 Supersymmetry
• Superconformal mechanics of AdS${}_2$ D-brane boundstates
• New realizations of the supergroup D(2,1;α) in N=4 superconformal mechanics
• Long multiplets in supersymmetric mechanics
• Deformed supersymmetric quantum mechanics with spin variables
• Multiparticle $\mathcal{N}=8$ mechanics with $F(4)$ superconformal symmetry
• Comments on HKT supersymmetric sigma models and their Hamiltonian reduction
• Minimal unitary representation of D(2,1;λ) and its SU(2) deformations and d=1, N=4 superconformal models
• Deformed $\mathcal{N}=8$ mechanics of $(8,8,0)$ multiplets
• On General Off-Shell Representations of Worldline (1D) Supersymmetry
• Supersymmetric Extension of Hopf Maps: N=4 sigma-models and the S^3 -> S^2 Fibration
• Superconformal Quantum Mechanics from M2-branes
• $\mathcal{N}=2$ supersymmetric hyperbolic Calogero-Sutherland model
• $\mathcal{N}=4$ supersymmetric Calogero-Sutherland models
• Generic N=4 supersymmetric hyper-Kähler sigma models in D=1
• Adinkras From Ordered Quartets of BC${}_4$ Coxeter Group Elements and Regarding 1,358,954,496 Matrix Elements of the Gadget
• Real and complex supersymmetric d=1 sigma models with torsions
• N=4 mechanics with diverse (4,4,0) multiplets: explicit examples of HKT, CKT, and OKT geometries
• Harmonic Superfields in N=4 Supersymmetric Quantum Mechanics
• Nahm equations in supersymmetric mechanics
• Quasicomplex N=2, d=1 Supersymmetric Sigma Models
• $\mathcal{N}=4$ Supersymmetric $d=1$ Sigma Models on Group Manifolds
• Bi-HKT and bi-Kaehler supersymmetric sigma models
• Dual multiplets in N=4 superconformal mechanics
• New Super Calogero Models and OSp(4|2) Superconformal Mechanics
• The geometry of gauged (super)conformal mechanics
• $\mathcal{N}=4$ supersymmetric $\mathrm{U}(2)$-spin hyperbolic Calogero-Sutherland model
• N=4, d=1 Supersymmetric Hyper-Kaehler Sigma Models with Isospin Variables
• SU$(2|1)$ supersymmetric spinning models of chiral superfields
• N=4, d=3 nonlinear electrodynamics
• Supersymmetric Calogero models from superfield gauging
• Relativistic generalization of the rational Calogero model
• Extended supersymmetry and its applications in quantum mechanical models associated with self-dual gauge fields