PT-Symmetric Non-Hermitian Quantum Field Theories with Supersymmetry

Abstract

We formulate supersymmetric non-Hermitian quantum field theories with PT symmetry, starting with free chiral boson/fermion models and then including trilinear superpotential interactions. We consider models with both Dirac and Majorana fermions, analyzing them in terms of superfields and at the component level. We also discuss the relation between the equations of motion, the (non-)invariance of the Lagrangian and the (non-)conservation of the supercurrents in the two models. We exhibit a similarity transformation that maps the free-field supersymmetric PT-symmetric Dirac model to a supersymmetric Hermitian theory, but there is, in general, no corresponding similarity transformation for the Majorana model. In this model, we find generically a mass splitting between bosons and fermions, even though its construction is explicitly supersymmetric, offering a novel non-Hermitian mechanism for soft supersymmetry breaking.

arXiv comment23 pages, revtex format; to match published version

References in corpus (33)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Supersymmetry and Quantum Mechanics
• Complex Extension of Quantum Mechanics
• Introduction to PT-Symmetric Quantum Theory
• Parity-time-symmetric quantum critical phenomena
• Resonant CP violation induced by particle mixing in transition amplitudes
• Supersymmetry and the spontaneous breakdown of PT symmetry
• Optical realization of relativistic non-Hermitian quantum mechanics
• Supersymmetry without hermiticity
• Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems
• Dual PT-Symmetric Quantum Field Theories
• Supersymmetric Laser Arrays
• Model of supersymmetric quantum field theory with broken parity symmetry
• Symmetries and conservation laws in non-Hermitian field theories
• Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories
• A light Higgs Boson would invite Supersymmmetry
• Relativistic Non-Hermitian Quantum Mechanics
• Goldstone bosons and the Englert-Brout-Higgs mechanism in non-Hermitian theories
• Non-Hermitian extension of gauge theories and implications for neutrino physics
• Goldstone bosons in different PT-regimes of non-Hermitian scalar quantum field theories
• Observation of Emergent Spacetime Supersymmetry at Superconducting Quantum Criticality
• Gauge invariance and the Englert-Brout-Higgs mechanism in non-Hermitian field theories
• Edge quantum criticality and emergent supersymmetry in topological phases
• Spontaneously Breaking Non-Abelian Gauge Symmetry in Non-Hermitian Field Theories
• Pseudo-Hermitian approach to Goldstone's theorem in non-Abelian non-Hermitian quantum field theories
• Non-Hermitian neutrino oscillations in matter with PT symmetric Hamiltonians
• Relativistic PT-symmetric fermionic theories in 1+1 and 3+1 dimensions
• Light neutrino masses from a non-Hermitian Yukawa theory
• Decay of the Higgs boson to ${\tau }^{-}{\tau }^{+}$ and non-Hermiticity of the Yukawa interaction
• On the construction of non-Hermitian Hamiltonians with all-real spectra through supersymmetric algorithms
• Consistent description of field theories with non-Hermitian mass terms
• Symmetry properties of non-Hermitian PT-symmetric quantum field theories
• An upper limit on fermion mass spectrum in non-Hermitian models and its implications for studying of dark matter

Cited by in corpus (18)

• Non-Hermitian Physics
• Discrete spacetime symmetries and particle mixing in non-Hermitian scalar quantum field theories
• Non-Hermitian Stark Many-Body Localization
• Symmetry-protected exceptional and nodal points in non-Hermitian systems
• PT symmetric fermionic field theories with axions: Renormalization and dynamical mass generation
• Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory
• IR/UV mixing from local similarity maps of scalar non-Hermitian field theories
• Poincaré symmetries and representations in pseudo-Hermitian quantum field theory
• Non-Hermitian Yukawa interactions of fermions with axions: potential microscopic origin and dynamical mass generation
• Non-Hermiticity: a new paradigm for model building in particle physics
• Wilsonian approach to the interaction ${\varphi }^2(i\varphi {)}^{\epsilon }$
• Complex Langevin Dynamics and Supersymmetric Quantum Mechanics
• Pseudo-Hermitian extensions of the harmonic and isotonic oscillators
• Ghosts in higher derivative Maxwell-Chern-Simon's theory and $\mathcal{P}\mathcal{T}-$symmetry
• Thermodynamic properties of non-Hermitian Nambu--Jona-Lasinio models
• Complex topological soliton with real energy in particle physics
• Oscillation probabilities for a PT-symmetric non-Hermitian two-state system
• Conformal bridge transformation, $\mathcal{P}\mathcal{T}$- and super- symmetry