Exactly solvable diffusion models in the framework of the extended supersymmetric quantum mechanics

This work is aimed at demonstrating the possibility to construct new exactly-solvable stochastic systems by use of the extended supersymmetric quantum mechanics (N=4SUSY QM) formalism. A feature of the proposed approach consists in the fact that obtained new potentials, which enter the Langevin equation, and so probability densities have a parametric freedom. The latter allows one to change the form of potentials without changing the temporal behavior of the probability densities.     

Bäcklund–Darboux transformations and discretizations of N = 2 a = −2 supersymmetric KdV equation

The $N=2a=?2$ supersymmetric KdV equation is studied. A Darboux transformation and the corresponding Bäcklund transformation are constructed for this equation. Also, a nonlinear superposition formula is worked out for the associated Bäcklund transformation. The Bäcklund transformation and the related nonlinear superposition formula are used to construct integrable super semi-discrete and full discrete systems. The continuum limits of these discrete systems are also considered.     

Non-hermitian Hamiltonians and the Painlevé IV equation with real parameters

In this Letter we will use higher-order supersymmetric quantum mechanics to obtain several families of complex solutions g(x;a,b) of the Painlevé IV equation with real parameters a,b. We shall also study the algebraic structure, the eigenfunctions and the energy spectra of the corresponding non-hermitian Hamiltonians.     

Algebraic solution of the supersymmetric hydrogen atom in d dimensions

In this paper the supersymmetric extension of the Schrödinger Hamiltonian with 1/r-potential in arbitrary space-dimensions is constructed. The supersymmetric hydrogen atom admits a conserved Laplace-Runge-Lenz vector which extends the rotational symmetry SO(d) to a hidden SO(d+1) symmetry. This symmetry of the system is used to determine the discrete eigenvalues with their degeneracies and the corresponding bound state wave functions.     

Non-decoupling effects in supersymmetric Higgs sectors

A wide class of Higgs sectors is investigated in supersymmetric standard models. When the lightest Higgs boson (h  ) looks the standard model one, the mass (mh$m_h$) and the triple Higgs boson coupling (the hhh   coupling) are evaluated at the one-loop level in each model. While mh$m_h$ is at most 120–130 GeV in the minimal supersymmetric standard model (MSSM), that in models with an additional neutral singlet or triplet fields can be much larger. The hhh coupling can also be sensitive to the models: while in the MSSM the deviation from the standard model prediction is not significant, that can be 30–60% in some models such as the MSSM with the additional singlet or with extra doublets and charged singlets. These models are motivated by specific physics problems like the μ-problem, the neutrino mass, the scalar dark matter and so on. Therefore, when h   is found at the CERN Large Hadron Collider, we can classify supersymmetric models by measuring mh$m_h$ and the hhh coupling accurately at future collider experiments.     

Higher dimensional supersymmetric quantum mechanics and Dirac equation

We exhibit the supersymmetric quantum mechanical structure of the full 3+1 dimensional Dirac equation considering ‘mass’ as a function of coordinates. Its usefulness in solving potential problems is discussed with specific examples. We also discuss the ‘physical’ significance of the supersymmetric states in this formalism.     

Painlevé IV coherent states

A simple way to find solutions of the Painlevé IV equation is by identifying Hamiltonian systems with third-order differential ladder operators. Some of these systems can be obtained by applying supersymmetric quantum mechanics (SUSY QM) to the harmonic oscillator. In this work, we will construct families of coherent states for such subset of SUSY partner Hamiltonians which are connected with the Painlevé IV equation. First, these coherent states are built up as eigenstates of the annihilation operator, then as displaced versions of the extremal states, both involving the related third-order ladder operators, and finally as extremal states which are also displaced but now using the so called linearized ladder operators. To each SUSY partner Hamiltonian corresponds two families of coherent states: one inside the infinite subspace associated with the isospectral part of the spectrum and another one in the finite subspace generated by the states created through the SUSY technique.     

Electroweak baryogenesis

After a short general introduction to baryogenesis — the creation of a baryon asymmetry in our universe (BAU) — I will highlight some old and more recent models of electroweak baryogenesis: modifications of the Standard Model (SM), in particular supersymmetric ones as the MSSM, NMSSM, nMSSM, BMSSM, νμMSSM. I will also stress the role of electric dipole moments (EDMs) in limiting the CP violation needed for baryogenesis.     

Dynamics of loops in superspace

The loop equation, analogous to the Makeenko-Migdal equation, is derived for the supersymmetric generalization of the Wilson loop for the supersymmetric (N = 1) gauge theory.     

Kink mass quantum shifts from SUSY quantum mechanics

In this paper a new version of the DHN (Dashen–Hasslacher–Neveu) formula, which is used to compute the one-loop order kink mass correction in (1+1)-dimensional scalar field theory models, is constructed. The new expression is written in terms of the spectral data coming from the supersymmetric partner operator of the second-order small kink fluctuation operator and allows us to compute the kink mass quantum shift in new models for which this calculation was out of reach by means of the old formula.     

Odd Hamiltonian structure for supersymmetric Sawada-Kotera equation

We study the supersymmetric N=1 hierarchy connected with the Lax operator of the supersymmetric Sawada-Kotera equation. This operator produces the physical equations as well as the exotic equations with odd time. The odd Bi-Hamiltonian structure for the N=1 supersymmetric Sawada-Kotera equation is defined. The product of the symplectic and implectic Hamiltonian operator gives us the recursion operator. In that way we prove the integrability of the supersymmetric Sawada-Kotera equation in the sense that it has the Bi-Hamiltonian structure. The so-called “quadratic” Hamiltonian operator of even order generates the exotic equations while the “cubic” odd Hamiltonian operator generates the physical equations.     

Partition functions for quantum gravity, black holes, elliptic genera and Lie algebra homologies

There is a remarkable connection between quantum generating functions of field theory and formal power series associated with dimensions of chains and homologies of suitable Lie algebras. We discuss the homological aspects of this connection with its applications to partition functions of the minimal three-dimensional gravities in the space-time asymptotic to AdS₃, which also describe the three-dimensional Euclidean black holes, the pure N=1 supergravity, and a sigma model on N-fold generalized symmetric products. We also consider in the same context elliptic genera of some supersymmetric sigma models. These examples can be considered as a straightforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of SL(2,Z)) to partition functions represented by means of formal power series that encode Lie algebra properties.     

Quantum geometry of fermionic strings

The formalism of the previous paper is extended to the case of supersymmetric strings. The effective theory which sums up fermionic surfaces is described by the supersymmetric Liouville equation. At D = 10 effective decoupling of the Liouville dilaton takes place and our theory coincides with the old ones. At D = 3 our theory is equilavent to the three-dimensional Ising model, which is thus reduced to the two-dimensional supersymmetric Liouville theory.     

Spectral properties in supersymmetric matrix models

We formulate a general sufficiency criterion for discreteness of the spectrum of both supersymmmetric and non-supersymmetric theories with a fermionic contribution. This criterion allows an analysis of Hamiltonians in complete form rather than just their semiclassical limits. In such a framework we examine spectral properties of various (1+0) matrix models. We consider the BMN model of M-theory compactified on a maximally supersymmetric pp-wave background, different regularizations of the supermembrane with central charges and a non-supersymmetric model comprising a bound state of N D2 with m D0. While the first two examples have a purely discrete spectrum, the latter has a continuous spectrum with a lower end given in terms of the monopole charge.     

The supersymmetric transfer matrix for linear chains with nondiagonal disorder

A study is made of the supersymmetric transfer matrix of then-orbital linear chain with Gaussian nondiagonal and diagonal disorder in the matrix (Hubbard-Stratonovich) variables. This formalism is applied to the one-point Green's function. Invariant functions of supersymmetric matrices are discussed in Section 3.Work supported by the Deutsche Forschungsgemeinschaft.     

Integrable extensions of N = 2 supersymmetric KdV hierarchy associated with the nonuniqueness of the roots of the Lax operator

We present new supersymmetric integrable extensions of the a = 4, N = 2 KdV hierarchy. The root of the supersymmetric Lax operator of the KdV equation is generalized, by including additional fields. This generalized root generates a new hierarchy of integrable equations, for which we investigate the Hamiltonian structure. In a special case our system describes the interaction of the KdV equation with the two MKdV equations.     

Algebraic Bethe ansatz for integrable Kondo impurities in the one-dimensional supersymmetric t-J model

An integrable Kondo problem in the one-dimensional supersymmetric t-J model is studied by means of the boundary supersymmetric quantum inverse scattering method. the boundary K matrices depending on the local moments of the impurities are presented as a nontrivial realization of the graded reflection equation algebras in a two-dimensional impurity Hilbert space. Further, the model is solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.