One-parameter nonrelativistic supersymmetry for microtubules

The one-parameter nonrelativistic supersymmetry of Mielnik [J. Math. Phys. 25 (1984) 3387] is applied to the simple supersymmetric model of Caticha [Phys. Rev. A 51 (1995) 4264] in the form used by Rosu [Phys. Rev. E 55 (1997) 2038] for microtubules. By this means, we introduce Montroll double-well potentials with singularities that move along the positive or negative traveling direction depending on the sign of the free parameter of Mielnik's method. Possible interpretations of the singularity are either microtubule associated proteins (motors) or structural discontinuities in the arrangement of the tubulin molecules.     

Hidden supersymmetry

Inspired by the concept of complementarity, we present a illustrative model for the weak interactions with unbroken gauge symmetry and unbroken supersymmetry. The observable particles are bound states of some more fundamental particles. Supersymmetry is broken at the macroscopic scale of the observable particles by a discrete symmetry but remains exact at the scale of the fundamental particle and is thus hidden. This provides a link between theories at very high energies and the observed particle physics. Supersymmetric particles are confined in usual matter.     

A geometric formulation of supersymmetry

The scalar fields of supersymmetric models are coordinates of a geometric space. We propose a formulation of supersymmetry that is covariant with respect to reparametrizations of this target space. Employing chiral multiplets as an example, we introduce modified supersymmetry variations and redefined auxiliary fields that transform covariantly under reparametrizations. The resulting action and transformation laws are manifestly covariant and highlight the geometric structure of the supersymmetric theory. The covariant methods are developed first for general theories (not necessarily supersymmetric) whose scalar fields are coordinates of a Riemannian target space.     

A class of partially solvable two-dimensional quantum models with periodic potentials

The supersymmetric approach is used to analyse a class of two-dimensional quantum systems with periodic potentials. In particular, the method of SUSY-separation of variables allowed us to find a part of the energy spectra and the corresponding wave functions (partial solvability) for several models. These models are not amenable to conventional separation of variables, and they can be considered as two-dimensional generalizations of Lamé, associated Lamé, and trigonometric Razavy potentials. All these models have the symmetry operators of fourth order in momenta, and one of them (the Lamé potential) obeys the property of self-isospectrality.     

Non-minimal and non-universal supersymmetry

I motivate and discuss non-minimal and non-universal models of supersymmetry and supergravity consistent with string unification at 10¹⁰ GeV.     

Infra-red fixed points in supersymmetry

Model independent constraints on supersymmetric models emerge when certain couplings are drawn towards their infra-red (quasi) fixed points in the course of their renormalization group evolution. The general principles are first reviewed and the conclusions for some recent studies of theories with R-parity and baryon and lepton number violations are summarized.     

B decays and supersymmetry

I discuss how supersymmetry affects various observables in B decays, and point out the interesting channels in the context of B factories.     

Finite-temperature supersymmetry: the Wess-Zumino model

We investigate the breakdown of supersymmetry at finite temperature. While it has been proven that temperature always breaks supersymmetry, the nature of this breaking is less clear. On the one hand, a study of the Ward-Takahashi identities suggests a spontaneous breakdown of supersymmetry without the existence of a Goldstino, while on the other hand it has been shown that in any supersymmetric plasma there should exist a massless fermionic collective excitation, the phonino. Aim of this work is to unify these two approaches. For the Wess-Zumino model, it is shown that the phonino exists and contributes to the supersymmetric Ward-Takahashi identities in the right way displaying that supersymmetry is broken spontaneously with the phonino as the Goldstone fermion.     

The status of supersymmetry phenomenology

In this brief review the following topics are discussed: Direct searches for SUSY in mSUGRA: a brief review of the relevant mass limits, the clean trilepton signal, the hunt for the third generation of sfermions, Direct searches beyond mSUGRA: search prospects in models with nonuniversal gaugino masses, search prospects in models with nonuniversal scalar masses, Indirect searches for SUSY: precision electroweak observables and SUSY, ε′/ε and SUSY.     

Polynomial supersymmetry for matrix Hamiltonians

We study intertwining relations for matrix non-Hermitian Hamiltonians by matrix differential operators of arbitrary order. It is established that for any intertwining operator of minimal order there is operator that intertwines the same Hamiltonians in the opposite direction and such that the products of these operators are identical polynomials of the corresponding Hamiltonians. The related polynomial algebra of supersymmetry is constructed. The problems of minimization and reducibility of a matrix intertwining operator are considered and the criteria of minimizability and reducibility are presented. It is shown that there are absolutely irreducible matrix intertwining operators, in contrast to the scalar case.     

Split supersymmetry in brane models

Type-I string theory in the presence of internal magnetic fields provides a concrete realization of split supersymmetry. To lowest order, gauginos are massless while squarks and sleptons are superheavy. For weak magnetic fields, the correct Standard Model spectrum guarantees gauge coupling unification with sin² ϑW=3/8 at the compactification scale of M _GUT ⋍ 2 × 10¹⁶ GeV. I discuss mechanisms for generating gaugino and higgsino masses at the TeV scale, as well as generalizations to models with split extended supersymmetry in the gauge sector.     

Mixing-induced spontaneous supersymmetry breaking

It is conjectured that flavor mixing furnishes a universal mechanism for the spontaneous breaking of supersymmetry. The conjecture is proved explicitly for the mixing of two chiral N=1 supermultiplets and arguments for its general validity are given. That is an instance of the O?Raifeartaigh Lagrangian for which there is no tree-level nor perturbative breaking. Nonetheless, the dynamical breaking occurs due to the vacuum condensate, a mixing-induced nonperturbative effect that lifts the zero point energy.     

Mechanisms of supersymmetry breaking in the minimal supersymmetric standard model

We provide a bird’s eyeview of current ideas on supersymmetry breaking mechanisms in the MSSM. The essentials of gauge, gravity, anomaly and gaugino/higgsino mediation mechanisms are covered briefly and the phenomenology of the associated models is touched upon. A few statement are also made on braneworld supersymmetry breaking.     

Constraints on sparticle spectrum in different supersymmetry breaking models

We derive sum rules for the sparticle masses in different models of supersymmetry breaking. This includes the gravity-mediated models (SUGRA models) as well as models in which supersymmetry breaking terms are induced by super-Weyl anomaly (AMSB models). These sum rules can help in distinguishing between these models. In particular, we obtain an upper bound on the mass of the lightest neutralino as a function of the gluino mass in SUGRA and AMSB models.     

Some aspects of R-parity violating supersymmetry

I briefly review a scenario where R-parity is explicitly broken through a term bilinear in the lepton and Higgs superfields in the superpotential. An immediate consequence of the presence of this term is the generation of a massive neutrino at the tree level. Constraints on the parameter space are discussed in the context of recent super-Kamiokande results on atmospheric neutrinos. The testability of such models is emphasized through the observation of comparable numbers of muons and taus, produced together with the H⁻-boson, in decays of the lightest neutralino. Some other phenomenological implications of such a scenario are also discussed.     

Naturalness,supersymmetry and implications for LHC and dark matter

It is shown that the Hyperbolic Branch of the radiative electroweak symmetry breaking contains in it three regions: the Focal Point, Focal Curves, and Focal Surfaces. Further, the Focal Point is shown to lie on the boundary of a Focal Curve. These focal regions allow for a small μ while scalar masses can become large and may lie in the several TeV region. It is shown that for the mSUGRA model the current LHC-7 constraint depletes the Focal Point region while regions on Focal Curves and Focal Surfaces remain largely intact. The LHC implications for models which lie on Focal Curves are briefly discussed as well as the implications of dark matter constraints for the Focal Point, Focal Curves and Focal Surfaces are discussed.     

Precision flavour physics and supersymmetry

We review the salient features of a comparative study of the profile of the CKM unitarity triangle, and the resulting CP-violating phases , β and γ in B decays, in the standard model and in several variants of the minimal supersymmetric standard model (MSSM), reported recently by us. These theories are characterized by a single phase in the quark flavour mixing matrix and give rise to well-defined contributions in the flavour-changing-neutral-current transitions in K and B decays. We analyse the supersymmetric contributions to the mass differences in the B_d⁰– and B_s⁰– systems, ΔM_d and ΔM_s, respectively, and to the CP-violating quantity || in K decays. Our analysis shows that the predicted ranges of β in the standard model and in MSSM models are very similar. However, precise measurements at B-factories and hadron machines may be able to distinguish these theories in terms of the other two CP-violating phases and γ.     

Supersymmetry in quantum mechanics

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable. In this lecture I review the theoretical formulation of supersymmetric quantum mechanics and discuss many of its applications. I show that the well-known exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric partner potentials and shape invariance. The connection between inverse scattering, isospectral potentials and supersymmetric quantum mechanics is discussed and multi-soliton solutions of the KdV equation are constructed. Further, it is pointed out that the connection between the solutions of the Dirac equation and the Schrödinger equation is exactly same as between the solutions of the MKdV and the KdV equations.     

Electroweak breaking and supersymmetry breaking

We discuss the clash between the absence of fine tuning in the Higgs potential and a sufficient suppression of flavour changing neutral current transitions in supersymmetric extensions of the standard model. It is pointed out that horizontalU(1) symmetry combined with theD-term supersymmetry breaking provides a realistic framework for solving both problems.     

Higher-order semiclassical energy expansions for potentials with non-integer powers

In this paper, we present a semiclassical eigenenergy expansion for the potential |x|^α when α is a positive rational number of the form2n/m (n is a positive integer and m is an odd positive integer). Remarkably, this expansion is found to be identical to the WKB expansion obtained for the potentialx ^N(N-even), if2n/m is replaced byN. Taking the limitm → 2 of the above expansion, we obtain an explicit asymptotic energy expansion of symmetric odd power potentials |x|^2j+1 (j- positive integer). We then show how to develop approximate semiclassical expansions for potentials |x|^α when α is any positive real number.