Supersymmetry of 𝒫𝒯-symmetric tridiagonal Hamiltonians

We extend the study of supersymmetric tridiagonal Hamiltonians to the case of non-Hermitian Hamiltonians with real or complex conjugate eigenvalues. We find the relation between matrix elements of the non-Hermitian Hamiltonian [Formula: see text] and its supersymmetric partner [Formula: see text] in a given basis. Moreover, the orthogonal polynomials in the eigenstate expansion problem attached to [Formula: see text] can be recovered from those polynomials arising from the same problem for [Formula: see text] with the help of kernel polynomials. Besides its generality, the developed formalism in this work is a natural home for using the numerically powerful Gauss quadrature techniques in probing the nature of some physical quantities such as the energy spectrum of [Formula: see text]-symmetric complex potentials. Finally, we solve the shifted [Formula: see text]-symmetric Morse oscillator exactly in the tridiagonal representation.

SUSY Searches with Taus at the LHC

The supersymmetric partner of the tau lepton, the stau, is predicted to be relatively light in a range of SUSY models and may be a key for dark matter. This talk presents recent ATLAS and CMS results from proton-proton collisions at \sqrt{s}s = 13 TeV corresponding to an integrated luminosity of 36.1 fb^{-1}−1 and 35.9 fb^{-1}−1 delivered by the LHC and recorded by the ATLAS and CMS detectors respectively in 2015 and 2016, to search for direct stau pair production, and indirect stau production mediated by other SUSY particles.

A solution to lithium problem by long-lived stau

We review a nonstandard Big-Bang Nucleosynthesis (BBN) scenario within the minimal supersymmetric standard model, and propose an idea to solve both the [Formula: see text] and [Formula: see text] problems. Each problem is a discrepancy between the predicted abundance in the standard BBN and observed one. We focus on the stau, a supersymmetric partner of tau lepton, which is a long-lived charged particle when it is the next lightest supersymmetric particle and is degenerate in mass with the lightest supersymmetric particle. The long-lived stau forms a bound state with a nucleus, and provides nonstandard nuclear reactions. One of those, the internal conversion process, accelerates the destruction of [Formula: see text] and [Formula: see text], and leads to a solution to the [Formula: see text] problem. On the other hand, the bound state of the stau and [Formula: see text] enhances productions of n, D, T and [Formula: see text]. The over-production of [Formula: see text] could solve the [Formula: see text] problem; while the over-productions of D and T could conflict with observations, and hence the relevant parameter space of the stau is strictly constrained. We therefore need to carefully investigate the stau–[Formula: see text] bound state to find a condition of solving the [Formula: see text] problem. The scenario of the long-lived stau simultaneously and successfully fits the abundances of light elements (D, T, [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]) and the neutralino dark matter to the observed ones. Consequently, the parameter space both of the stau and the neutralino is determined with excellent accuracy.

Exact Solutions of the Dirac Hamiltonian on the Sphere under Hyperbolic Magnetic Fields

Two-dimensional massless Dirac Hamiltonian under the influence of hyperbolic magnetic fields is mentioned in curved space. Using a spherical surface parameterization, the Dirac operator on the sphere is presented and the system is given as two supersymmetric partner Hamiltonians which coincides with the position dependent mass Hamiltonians. We introduce two ansatzes for the component of the vector potential to acquire effective solvable models, which are Rosen-Morse II potential and the model given Midya and Roy, whose bound states are JacobiX1type polynomials, and we adapt our work to these special models under some parameter restrictions. The energy spectrum and the eigenvectors are found for Rosen-Morse II potential. On the other hand, complete solutions are given for the second system. The vector and the effective potentials with their eigenvalues are sketched for each system.

TOWARD A SUPERGRAVITY SPECTRAL ACTION

A spectral action for a generalized bosonic sector corresponding to the Dirac operator of Euclidean supergravity is proposed. We calculate, up to a4, the Seeley–DeWitt coefficients in the expansion of the spectral action. It is in general not known how to construct a "matter fermionic" supersymmetric partner to the spectral action. The action we propose provides the effective action to be completed to get, at any order of the expansion, the corresponding supersymmetric action.

INHOMOGENEOUS BAROTROPIC FRW COSMOLOGIES IN CONFORMAL TIME

It is known that the barotropic FRW system of differential equations for zero cosmological constant can be reduced to simple harmonic oscillator (HO) differential equations in the conformal time variable. This is due to the fact that the Hubble rate parameter in conformal time is the solution of a simple Riccati equation of constant coefficients. In previous works, we have used this mathematical result to set the barotropic HO equations in the nonrelativistic supersymmetric approach by factorizing them. If a constant additive parameter, denoted by S, is added to the common Riccati solution of these supersymmetric partner cosmologies one obtains inhomogeneous barotropic cosmologies with periodic singularities in their spatial curvature indices that are counterparts of the non-shifted supersymmetric partners. The zero-mode solutions of these cyclic singular cosmologies are reviewed here as a function of real and imaginary shift parameter. We also notice the modulated zero modes obtained by using the general Riccati solution and comment on their cosmological application.