Perfectly invisible \( \mathcal{P}\mathcal{T} \) -symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry

Abstract

We investigate a special class of the \( \mathcal{P}\mathcal{T} \) -symmetric quantum models being perfectly invisible zero-gap systems with a unique bound state at the very edge of continuous spectrum of scattering states. The family includes the \( \mathcal{P}\mathcal{T} \) -regularized two particle Calogero systems (conformal quantum mechanics models of de Alfaro-Fubini-Furlan) and their rational extensions whose potentials satisfy equations of the KdV hierarchy and exhibit, particularly, a behaviour typical for extreme waves. We show that the two simplest Hamiltonians from the Calogero subfamily determine the fluctuation spectra around the \( \mathcal{P}\mathcal{T} \)-regularized kinks arising as traveling waves in the field-theoretical Liouville and SU(3) conformal Toda systems. Peculiar properties of the quantum systems are reflected in the associated exotic nonlinear supersymmetry in the unbroken or partially broken phases. The conventional \( \mathcal{N}=2 \) supersymmetry is extended here to the \( \mathcal{N}=4 \) nonlinear supersymmetry that involves two bosonic generators composed from Lax-Novikov integrals of the subsystems, one of which is the central charge of the superalgebra. Jordan states are shown to play an essential role in the construction.

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Correspondence to Mikhail S. Plyushchay.

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Guilarte, J.M., Plyushchay, M.S. Perfectly invisible \( \mathcal{P}\mathcal{T} \) -symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry. J. High Energ. Phys. 2017, 61 (2017). https://doi.org/10.1007/JHEP12(2017)061

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Keywords

  • Conformal and W Symmetry
  • Discrete Symmetries
  • Extended Supersymmetry
  • Integrable Hierarchies