Hamiltonian structure and coset construction of the supersymmetric extensions of N=2 KdV hierarchy

A manifestly N=2 supersymmetric coset formalism is applied to analyse the "fermionic" extensions of N=2 $a=4$ and $a=-2$ KdV hierarchies. Both these hierarchies can be obtained from a manifest N=2 coset construction. This coset is defined as the quotient of some local but non-linear superalgebra by a $\hat{U(1)}$ subalgebra. Three superextensions of N=2 KdV hierarchy are proposed, among which one seems to be entirely new.Comment: 11 pages, Latex, a few modifications in the tex

The W(sl(N+3),sl(3)) algebras and their contractions to W3

We construct the nonlinear $W(sl(N+3),sl(3))$ algebras and find the spectrum of values of the central charge that gives rise, by contracting the $W(sl(N+3),sl(3))$ algebras, to a $W_3$ algebra belonging to the coset $W((sl(N+3),sl(3))/(u(1)\oplus sl(N))$. Part of the spectrum was conjectured before, but part of it is given here for the first time. Using the tool of embedding the $W(sl(N+3),sl(3))$ algebras into linearizing algebras, we construct new realizations of $W_3$ modulo null fields. The possibility to predict, within the conformal linearization framework, the central charge spectrum for minimal models of the nonlinear $W(sl(N+3),sl(3))$ algebras is discussed at the end.Comment: 12 pages, 2 tables, LaTeX, minor typos corrected on pages 4 and

Null Fields Realizations of W3W_3 from W(sl(4),sl(3))W(sl(4),sl(3)) and W(sl(3∣1),sl(3))W(sl(3|1),sl(3)) Algebras

We consider the nonlinear algebras $W(sl(4),sl(3))$ and $W(sl(3|1),sl(3))$ and find their realizations in terms of currents spanning conformal linearizing algebras. The specific structure of these algebras, allows us to construct realizations modulo null fields of the $W_3$ algebra that lies in the cosets $W(sl(4),sl(3))/u(1)$ and $W(sl(3|1),sl(3))/u(1)$. Such realizations exist for the following values of the $W_3$ algebra central charge: $c_W=-30,-40/7,-98/5,-2$. The first two values are listed for the first time, whereas for the remaining values we get the new realizations in terms of an arbitrary stress tensor and $u(1)\times sl(2)$ affine currents.Comment: Submitted to Phys. Lett. B; PACS-no 11.30.L

N=4 Supersymmetric MICZ-Kepler systems on S3

Proceeding from the superfield action for $N=4, d=1$ nonlinear supermultiplet, equipped with the most general potential term, we find the action describing a charged particle on the sphere $S^3$ in the field of $n$ fixed Dirac dyons. We construct the supercharges and Hamiltonian and analyze some particulary interesting potentials corresponding to the N=4 supersymmetric extension of the integrable one- and two-center McIntosh--Cisneros--Zwanziger--Kepler (MICZ-Kepler) systems on $S^3$.Comment: 8 pages, PACS: 11.30.Pb, 03.65.-w; corrected a misprint in (3.12), added the last sentence on page 3, added the paragraph after (3.7), added the sentence after (4.5

Baryon resonance production in the π+d\pi+d reaction and search for η\eta-mesic nuclei at J-PARC

A double-scattering reaction $\pi^+ + d\to p + p + \eta$, where an $\eta$ meson is rescattered, may provide new information on the $\eta N\to \eta N$ scattering. An idea to measure this reaction is proposed. Moreover, experimental search for $\eta$-mesic nuclei by the same $(\pi, N)$ reaction is discussed.Comment: Talk given at the Workshop on "Hadron and Nuclear Physics (HNP09)", RCNP, Osaka, Japan, Nov. 16-19, 2009. To appear in the proceeding