We adress the problem of Fock space representations of (free) multiplet component fiels encountered in supersymmetric quantum field theory insisting on positivity and causality. We look in detail on the scalar and Majorana components of the chiral supersymmetric multiplet. Several Fock space representations are introduced. The last section contains a short application to the supersymmetric Epst...

We study the recently introduced Krein structure (indefinite metric) of the N = 1 supersymmetry and present the way into physical applications outside path integral methods. From the mathematical point of view some perspectives are mentioned at the end of the paper.

I discuss recent work with Anatoly Konechny proving a gradient formula for the boundary beta function of the general supersymmetric one-dimensional quantum system with boundary that is critical in the bulk but not at the boundary. I concentrate on some unanswered questions about which Aliosha expressed curiousity. PACS numbers: 11.10.Hi, 11.10.Kk, 11.10.Wx, 11.25.Uv, 64.60.fd One-dimensional qu...

We discuss the connection between supersymmetric field theories and topological field theories and show how this connection may be used to construct local lattice field theories which maintain an exact supersymmetry. It is shown how metric independence of the continuum topological field theory allows us to derive the lattice theory by blocking out of the continuum in a deformed geometry. This, ...

Reducing Supersymmetric Yang-Mills Field Theory to a single point in the three dimensional space results in the Supersymmetric Yang-Mills Quantum Mechanics (SYMQM) which basically is the effective quantum mechanics of zero momentum modes of the original theory. Such a system is still quite non-trivial and usually inherits many properties of the original field theory. In this talk some beautiful...

We show that there are solitons with fractional fermion number in integrable N=2 supersymmetric models. We obtain the soliton S-matrix for the minimal, N=2 supersymmetric theory perturbed in the least relevant chiral primary field, the Φ(1,3) superfield. The perturbed theory has a nice Landau-Ginzburg description with a Chebyshev polynomial superpotential. We show that the S-matrix is a tensor ...

We study various three-dimensional supersymmetric Maxwell Chern-Simons solitons by using type IIB brane configurations. We give a systematic classification of soliton spectra such as topological BPS vortices and nontopological vortices in N = 2, 3 supersymmetric Maxwell Chern-Simons system via the branes of type IIB string theory. We identify the brane configurations with the soliton spectra of...

These lectures briefly introduce dualities in four-dimensional quantum field theory, and summarize results found in supersymmetric field theories. The first lecture describes physical aspects of electric-magnetic (EM), strong-weak coupling (S), and infrared (IR) dualities. The second lecture focuses on results and conjectures concerning S-duality in N=2 supersymmetric gauge theories. The third ...