We propose a complete, d=6 covariant and kappa-symmetric, action for an M-theory five-brane propagating in D = 11 supergravity background.

We demonstrate how a Lorentz covariant formulation of the chiral p-form model in D = 2(p + 1) containing infinitely many auxiliary fields is related to a Lorentz covariant formulation with only one auxiliary scalar field entering a chiral p-form action in a nonpolynomial way. The latter can be regarded as a consistent Lorentz-covariant truncation of the former. We make the Hamiltonian analysis of the model based on the nonpolynomial action and show that the Dirac constraints have a simple form and are all of the first class. In contrast to the Siegel model the constraints are not the square of second-class constraints. The canonical Hamiltonian is quadratic and determines energy of a single chiral p-form. In the case of d = 2 chiral scalars the constraint can be improved by use of a 'twisting' procedure (without the loss of the property to be of the first class) in such a way that the central charge of the quantum constraint algebra is zero. This points to possible absence of anomaly in an appropriate quantum version of the model. 11. 15-q, 11.17+y

We propose a complete Born-Infeld-like action for a bosonic 5-brane with a worldvolume chiral field in a background of gravitational and antisymmetric gauge fields of D = 11 supergravity. When the five-brane couples to a three-rank antisymmetric gauge field, local symmetries of the five-brane require the addition to the action of an appropriate Wess-Zumino term. To preserve general coordinate and Lorentz invariance of the model we introduce a single auxiliary scalar field. The auxiliary field can be eliminated by gauge fixing a corresponding local symmetry at the price of the loss of manifest d = 6 worldvolume covariance. The double dimensional reduction of the five-brane model results in the Born-Infeld action with the Wess-Zumino term for a D = 10 four-D-brane.

We perform a generalization of the geometrical approach to describing extended objects for studying the doubly supersymmetric twistor{like formulation of super{p{branes. Some basic features of embedding world supersurface into target superspace speci ed by a geometrodynamical condition are considered. It is shown that the main attributes of the geometrical approach, such as the second fundamental form and extrinsic torsion of the embedded surface, and the Codazzi, Gauss and Ricci equations, have their doubly supersymmetric counterparts. At the same time the embedding of supersurface into target superspace has its particular features. For instance, the embedding may cause more rigid restrictions on the geometrical properties of the supersurface. This is demonstrated with the examples of an N=1 twistor{like supermembrane in D=11 and type II superstrings in D=10, where the geometrodynamical condition causes the embedded supersurface to be minimal and puts the theories on the mass shell.

The authors study Weyl symmetry from a cohomological point of view in theories including gravity in order to determine 0- and 1-cocycles (Weyl invariants and Weyl anomalies). For pedagogical reasons they rederive known results in four dimensions. Then they solve the same problem in six dimensions. The relation of Weyl anomalies to cocycles of the diffeomorphisms are determined: they can be obtained from each other by subtracting a suitable counterterm from the action. Finally it is shown by an example that such a subtraction corresponds to changing the regularisation scheme.

We consider a space-time invariant duality symmetric action for a free Maxwell field and an SL(2, R) × SO(6, 22) invariant effective action describing a low-energy bosonic sector of the heterotic string compactified on a six-dimensional torus. The manifest Lorentz and general coordinate invariant formulation of the models is achieved by coupling dual gauge fields to an auxiliary vector field from an axionic sector of the theory.

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