Fermionic Shift Symmetries in (Anti) de Sitter Space

Abstract

We study extended shift symmetries that arise for fermionic fields on anti-de Sitter (AdS) space and de Sitter (dS) space for particular values of the mass relative to the curvature scale. We classify these symmetries for general mixed-symmetry fermionic fields in arbitrary dimension and describe how fields with these symmetries arise as the decoupled longitudinal modes of massive fermions as they approach partially massless points. For the particular case of AdS${}_4$, we look for non-trivial Lie superalgebras that can underly interacting theories that involve these fields. We study from this perspective the minimal such theory, the Akulov--Volkov theory on AdS${}_4$, which is a non-linear theory of a spin-$1/2$ Goldstino field that describes the spontaneous breaking of $\mathcal{N}=1$ supersymmetry on AdS${}_4$ down to the isometries of AdS${}_4$. We show how to write the nonlinear supersymmetry transformation for this theory using the fermionic ambient space formalism. We also study the Lie superalgebras of candidate multi-field examples and rule out the existence of a supersymmetric special galileon on AdS${}_4$.

40 pages, 2 figures

References in corpus (23)

• Effective Field Theories from Soft Limits
• A Periodic Table of Effective Field Theories
• Symmetries for Galileons and DBI scalars on curved space
• Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism
• Galileons as Wess-Zumino Terms
• General Embedded Brane Effective Field Theories
• DBI Realizations of the Pseudo-Conformal Universe and Galilean Genesis Scenarios
• Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: II. Oscillator Realization
• Gauge fields in (anti)-de Sitter space and Connections of its symmetry algebra
• Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions
• de Sitter tachyons and related topics
• Frame-like Actions for Massless Mixed-Symmetry Fields in Minkowski space. Fermions
• Flato-Fronsdal theorem for higher-order singletons
• Geometry of Special Galileon
• Frame-like gauge invariant formulation for mixed symmetry fermionic fields
• Lagrangian formulation of massive fermionic totally antisymmetric tensor field theory in AdS_d space
• Uniformizing higher-spin equations
• Exceptional scalar theories in de Sitter space
• Note on antisymmetric spin-tensors
• Higher-spin charges in Hamiltonian form. II. Fermi fields
• Shift Symmetries for p-Forms and Mixed Symmetry Fields on (A)dS
• Dynamics of (SUSY) AdS Space Isometry Breaking
• $N=1$ Supergravitational Heterotic Galileons

Cited by in corpus (2)

• Hidden Conformal Symmetry of the Discrete Series Scalars in dS${}_2$
• Dualities Among Massive, Partially Massless and Shift Symmetric Fields on (A)dS