Introduction to the Classical Theory of Higher Spins

We review main features and problems of higher spin field theory and flash some ways along which it has been developed over last decades.Comment: JHEP Style, 32 pages; v2 typos corrected, comments and references added; v3 new material in Section 3 and refs. added, version published in AIP Conf.Proc. 767(2005)17

Introduction to the Superembedding Description of Superbranes

Basics of the geometrical formulation of the dynamics of supersymmetric objects are considered and its relation to conventional formulations of superbranes is discussed. In particular, we demonstrate how the kappa-symmetry of the Green-Schwarz formulation shows up from local worldvolume supersymmetry, and briefly discuss applications of the superembedding approach.Comment: LaTeX2e file, 11 pages. Invited lecture given at the XXXVII Karpacz Winter School "New Developments in Fundamental Interactions Theories" (February 6-15, 2000, Karpacz, Poland). To be published in Proceeding

Coincident (Super)-Dp-Branes of Codimension One

We consider properties of a covariant worldvolume action for a system of N coincident Dp-branes in D=(p+2) dimensional space-time (so called codimension one branes). In the case of N coincident D0-branes in D=2 we then find a generalization of this action to a model which includes fermionic degrees of freedom and is invariant under target-space supersymmetry and worldline kappa-symmetry. We find that the type IIA D=2 superalgebra generating the supersymmetry transformations of the ND0-brane system acquires a non-trivial "central extension" due to a nonlinear contribution of U(N) adjoint scalar fields. Peculiarities of space-time symmetries of coincident Dp-branes are discussed.Comment: LaTeX2e file, 14 pages. Some signs corrected. Version published in JHE

Can Chern-Simons or Rarita-Schwinger be a Volkov-Akulov Goldstone?

We study three-dimensional non-linear models of vector and vector-spinor Goldstone fields associated with the spontaneous breaking of certain higher-spin counterparts of supersymmetry whose Lagrangians are of a Volkov-Akulov type. Goldstone fields in these models transform non-linearly under the spontaneously broken rigid symmetries. We find that the leading term in the action of the vector Goldstone model is the Abelian Chern-Simons action whose gauge symmetry is broken by a quartic term. As a result, the model has a propagating degree of freedom which, in a decoupling limit, is a quartic Galileon scalar field. The vector-spinor goldstino model turns out to be a non-linear generalization of the three-dimensional Rarita-Schwinger action. In contrast to the vector Goldstone case, this non-linear model retains the gauge symmetry of the Rarita-Schwinger action and eventually reduces to the latter by a non-linear field redefinition. We thus find that the free Rarita-Schwinger action is invariant under a hidden rigid supersymmetry generated by fermionic vector-spinor operators and acting non-linearly on the Rarita-Schwinger goldstino.Comment: 24 pages, v2: in Conclusion added action for a 3d gravity model with two spin-2 gauge fields interacting via Lorentz connection, references added; v3: typos correcte