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

Gauging Nonlinear Supersymmetry

Coset methods are used to construct the action describing the dynamics associated with the spontaneous breaking of the local supersymmetries. The resulting action is an invariant form of the Einstein-Hilbert action, which in addition to the gravitational vierbein, also includes a massive gravitino field. Invariant interactions with matter and gauge fields are also constructed. The effective Lagrangian describing processes involving the emission or absorption of a single light gravitino is analyzed.Comment: 20 pages, no figure

Supergravity before and after 1976

This paper is part of the lecture given at the TH Division of CERN and devoted to the CXXV anniversary of the birthday of Elie Cartan (1869-1951). It is shown how the methods of differential geometry, due to E. Cartan, were applied to the construction of the supersymmetry transformation law and to the actions for Goldstone fermions and supergravity.Comment: 8 pages, latex, CERN-TH.7226/9

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

Phenomenology of Goldstino Couplings

A general coupling of the Goldstino to the matter field and the weak gravitational field is constructed based on the standard and the nonlinear Volkov-Akulov realization of SUSY. The resulting Lagrangian, which is invariant under SUSY transformations, can give rise to explicit interactions which couple the helicity +-1/2 states of the gravitino with the gravitational field as well as the matter field.Comment: 7 pages; final version to appear in Modern Physics Letters

Excited scalar mesons in a chiral quark model

First radial excitations of the isoscalar and isovector scalar mesons f_0(400-1200), f_0(980) and a_0(980) are investigated in the framework of a nonlocal version of a chiral quark model of the Nambu--Jona-Lasinio type. It is shown that f_0(1370), f_J(1710) and a_0(1450) are the first radially excited states of f_0(400-1200), f_0(980) and a_0(980) which are ground states of the scalar meson nonet. The mesons' masses and strong decay widths are calculated. The scalar resonance f_0(1500) is supposed to be a glueball. The status of K_0^*(1430) is discussed.Comment: LaTeX, 1 figure, minor misprints eradicate