On the cancellation of 4-derivative terms in the Volkov-Akulov action

Recently Kuzenko and McCarty observed the cancellation of 4-derivative terms in the $D=4 {\cal N}=1$ Volkov-Akulov supersymmetric action for the fermionic Nambu-Goldstone field. Here is presented a simple algebraic proof of the cancellation based on using the Majorana bispinors and Fiertz identities. The cancellation shows a difference between the Volkov-Akulov action and the effective superfield action recently studied by Komargodski and Seiberg and containing one 4-derivative term. We find out that the cancellation effect takes place in coupling of the Nambu-Goldstone fermion with the Dirac field. Equivalence between the KS and the VA Lagrangians is proved up to the first order in the interaction constant of the NG fermions.Comment: 18 pages; the version accepted for publication in Phys. Rev. D; new section regarding the proof of the equivalence between the Komargodski-Seiberg and the Volkov-Akulov actions is added: some comments and new references are include

The Tomonaga-Luttinger Model and the Chern-Simons Theory for the Edges of Multi-layer Fractional Quantum Hall Systems

Wen's chiral Tomonaga-Luttinger model for the edge of an m-layer quantum Hall system of total filling factor nu=m/(pm +- 1) with even p, is derived as a random-phase approximation of the Chern-Simons theory for these states. The theory allows for a description of edges both in and out of equilibrium, including their collective excitation spectrum and the tunneling exponent into the edge. While the tunneling exponent is insensitive to the details of a nu=m/(pm + 1) edge, it tends to decrease when a nu=m/(pm - 1) edge is taken out of equilibrium. The applicability of the theory to fractional quantum Hall states in a single layer is discussed.Comment: 15 page

Even and odd symplectic and K\"ahlerian structures on projective superspaces

Supergeneralization of \DC P(N) provided by even and odd K\"ahlerian structures from Hamiltonian reduction are construct.Operator $\Delta$ which used in Batalin-- Vilkovisky quantization formalism and mechanics which are bi-Hamiltonian under corresponding even and odd Poisson brackets are considered.Comment: 19 page

Nonlinear Realizations of Supersymmetry and Other Symmetries

Simultaneous nonlinear realizations of spontaneously broken supersymmetry in conjunction with other spontaneous and/or explicitly broken symmetries including R symmetry, global chiral symmetry, dilatations and the superconformal symmetries is reviewed.Comment: 15 pages, invited brief review for Mod. Phys. Lett.

Pion Polarizability in the NJL model and Possibilities of its Experimental Studies in Coulomb Nuclear Scattering

The charge pion polarizability is calculated in the Nambu-Jona-Lasinio model, where the quark loops (in the mean field approximation) and the meson loops (in the $1/N_c$ approximation) are taken into account. We show that quark loop contribution dominates, because the meson loops strongly conceal each other. The sigma-pole contribution $(m^2_\sigma-t)^{-1}$ plays the main role and contains strong t-dependence of the effective pion polarizability at the region $|t|\geq 4M_\pi^2$. Possibilities of experimental test of this sigma-pole effect in the reaction of Coulomb Nuclear Scattering are estimated for the COMPASS experiment.Comment: 11 pages, 8 figure

The processes e+e−→ππ(π′)e^{+}e^{-} \to \pi\pi(\pi') in the extended NJL model

The process $e^{+}e^{-} \to \pi^{+}\pi^{-}$ is described in the framework of the extended NJL model. Intermediate vector mesons $\rho^0(770)$, $\omega(782)$ and \rho'(1450)$are taken into account. Our results are in satisfactory agreement with experimental data. The prediction for the process$e^{+}e^{-} \to \pi\pi'(1300)$is given. Here the main contribution is given by the diagram with intermediate$\rho'(1450)$ meson.Comment: 7 pages, 5 figure

τ−→π−π0ντ\tau^{-} \to \pi^{-} \pi^{0} \nu_\tau decay in the extended NJL model

The width of the decay $\tau^{-} \to \pi^{-} \pi^{0} \nu_\tau$ was calculated in the extended NJL model. Contact interaction of $W$ boson with pion pair as well as the contribution of the $\rho$ mesons in ground and first radial-exited states are taken into account. The sum of the contact diagram and diagram with intermediate $\rho$ meson in the ground state leads to the result which coincides with the result of the vector-dominance model. Our results are in satisfactory agreement with experimental data.Comment: 5 pages, 3 figures, 1 tabl