Christian R. Preitschopf

OSp supergroup manifolds, superparticles, and supertwistors

We construct simple twistor-like actions describing superparticles propagating on a coset superspace OSp(1|4)/SO(1,3) (containing the D=4 anti-de-Sitter space as a bosonic subspace), on a supergroup manifold OSp(1|4) and, generically, on OSp(1|2n). Making two different contractions of the superparticle model on the OSp(1|4) supermanifold we get massless superparticles in Minkowski superspace without and with tensorial central charges. Using a suitable parametrization of OSp(1|2n) we obtain even Sp(2n)-valued Cartan forms which are quadratic in Grassmann coordinates of OSp(1|2n). This result may simplify the structure of brane actions in super-AdS backgrounds. For instance, the twistor-like actions constructed with the use of the even OSp(1|2n) Cartan forms as supervielbeins are quadratic in fermionic variables. We also show that the free bosonic twistor particle action describes massless particles propagating in arbitrary space-times with a conformally flat metric, in particular, in Minkowski space and AdS space. Applications of these results to the theory of higher spin fields and to superbranes in AdS superbackgrounds are mentioned.

DUALITY OF SELF-DUAL ACTIONS

Abstract Using examples of a D = 2 chiral scalar and a duality-symmetric formulation of D = 4 Maxwell theory we study duality properties of actions for describing chiral bosons. In particular, in the D = 4 case, upon performing a duality transformation of an auxiliary scalar field, which ensures Lorentz covariance of the action, we arrive at a new covariant duality-symmetric Maxwell action, which contains a two-form potential as an auxiliary field. When the two-form field is gauge fixed this action reduces to a duality-symmetric action for Maxwell theory constructed by Zwanziger. We consider properties of this new covariant action and discuss its coupling to external dyonic sources. We also demonstrate that the formulations considered are self-dual with respect to a dualization of the field strengths of the chiral fields.

Conformal Field Theory in Conformal Space

We present a new framework for a Lagrangian description of conformal field theories in various dimensions based on a local version of d + 2-dimensional conformal space. The results include a true gauge theory of conformal gravity in d = (1, 3) and any standard matter coupled to it. An important feature is the automatic derivation of the conformal gravity constraints, which are necessary for the analysis of the matter systems.

Osp(1|8)-gravity

Abstract We analyse a new MacDowell-Mansouri R 2 -type supergravity action based on the superalgebra Osp (1|8). This contribution summarizes the work of ref. [1].

On a possible new R**2 theory of supergravity

We consider a new MacDowell-Mansouri R{sup 2}-type supergravity theory, an extension of conformal supergravity, based on the superalgebra Osp(1{vert_bar}8). Invariance under local symmetries with negative Weyl weight is achieved by imposing chirality-duality and double-duality constraints on curvatures, along with the usual constraint of vanishing supertorsion. An analysis of the remaining gauge symmetries shows that those with vanishing Weyl weight are invariances of the action at the linearized level. For the symmetries with positive Weyl weight we find that invariance of the action would require further modifications of the transformation rules. This conclusion is supported by a kinematical analysis of the closure of the gauge algebra. {copyright} {ital 1997} {ital The American Physical Society}

Possible new R{sup 2} theory of supergravity

We consider a new MacDowell-Mansouri R{sup 2}-type supergravity theory, an extension of conformal supergravity, based on the superalgebra Osp(1{vert_bar}8). Invariance under local symmetries with negative Weyl weight is achieved by imposing chirality-duality and double-duality constraints on curvatures, along with the usual constraint of vanishing supertorsion. An analysis of the remaining gauge symmetries shows that those with vanishing Weyl weight are invariances of the action at the linearized level. For the symmetries with positive Weyl weight we find that invariance of the action would require further modifications of the transformation rules. This conclusion is supported by a kinematical analysis of the closure of the gauge algebra. {copyright} {ital 1997} {ital The American Physical Society}

Duality and Selfduality of Chiral Boson Fields in Various Dimensions

Duality-symmetric and self-dual fields (chiral bosons) are an important part of various theoretical models which are considered in the modern superstring theory. For a long period of time there has been a problem of how to construct an action for such fields which would simultaneously possess both duality symmetry and Lorentz-covariance.