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We study the tensor gauge fields ("notophs") of ungauged N =8, D =4 supergravity in superspace. These are described by 2-form potentials B2G in the adjoint representation of G =E7 (+7). The consistency of the natural candidates for the superspace constraints for their field strengths H3G fixes the form of the generalized Bianchi identities D H3G=... and also requires the potentials B2G/H with indices of G/H =E7 (+7)/S U (8) generators to be dual to the scalars of the N =8, D =4 supergravity multiplet. In contrast, the field strengths of the 2-form potentials corresponding to the S U (8) generators are dual to fermionic bilinears, so that these potentials are auxiliary rather than physical fields. Their presence, however, is essential to formulate a tensor hierarchy of N =8, D =4 supergravity consistent with its U-duality group E7(+7). [ABSTRACT FROM AUTHOR]

We construct the duality-symmetric actions for a large class of six-dimensional models describing hierarchies of non-Abelian scalar, vector and tensor fields related to one another by first-order (self-)duality equations that follow from these actions. In particular, this construction provides a Lorentz invariant action for non-Abelian self-dual tensor fields. The class of models includes the bosonic sectors of the 6d (1,0) superconformai models of interacting non-Abelian self-dual tensor, vector, and hypermultiplets. [ABSTRACT FROM AUTHOR]

We study the properties of the covariant supersymmetric and ?-symmetric action for a system of N nearly coincident M0-branes (mM0 system) in flat 11-dimensional (11D) superspace and obtain supersymmetric equations for this dynamical system. Although a single M0-brane is the massless 11D superparticle, center-of-energy motion of the mM0 system is characterized by a non-negative constant mass M constructed from the matrix fields describing the relative motion of mM0 constituents. We show that a bosonic solution of the mM0 equations can be supersymmetric iff this effective mass vanishes, M²=0, and that all the supersymmetric bosonic solutions preserve just one half of the 11D supersymmetry. [ABSTRACT FROM AUTHOR]

We obtain the Matrix model equations in the background of the maximally supersymmetric p-wave solution of the 11D supergravity and discuss its relation with the Berenstein-Maldacena-Nastase model. [ABSTRACT FROM AUTHOR]

All nonlinear extensions of the source-free Maxwell equations preserving both SO(2) electromagnetic duality invariance and conformal invariance are found, and shown to be limits of a one-parameter generalization of Born-Infeld electrodynamics. The strong-field limit is the same as that found by Bialynicki-Birula from Born-Infeld theory but the weak-field limit is a new one-parameter extension of Maxwell electrodynamics, which is interacting but admits exact light-velocity plane-wave solutions of arbitrary polarization. Small-amplitude waves on a constant uniform electromagnetic background exhibit birefringence, but one polarization mode remains lightlike. [ABSTRACT FROM AUTHOR]

We construct the duality-symmetric actions for a large class of six-dimensional models describing hierarchies of non-Abelian scalar, vector and tensor fields related to one another by first-order (self-)duality equations that follow from these actions. In particular, this construction provides a Lorentz invariant action for non-Abelian self-dual tensor fields. The class of models includes the bosonic sectors of the 6d (1,0) superconformal models of interacting non-Abelian self-dual tensor, vector, and hypermultiplets. [ABSTRACT FROM AUTHOR]