Martin Cederwall

The Dirichlet super-p-branes in ten-dimensional type IIA and IIB supergravity

We give the full supersymmetric and kappa-symmetric actions for the Dirichlet p-branes, including their coupling to background superfields of ten-dimensional type IIA and IIB supergravity.

The Dirichlet Super-Three-Brane in Ten-Dimensional Type IIB Supergravity

We give the full supersymmetric and kappa-symmetric action for the Dirichlet three-brane, including its coupling to background superfields of ten-dimensional type IIB supergravity.

The gauge structure of generalised diffeomorphisms

A bstractWe investigate the generalised diffeomorphisms in M-theory, which are gauge transformations unifying diffeomorphisms and tensor gauge transformations. After giving an En(n)-covariant description of the gauge transformations and their commutators, we show that the gauge algebra is infinitely reducible, i.e., the tower of ghosts for ghosts is infinite. The Jacobiator of generalised diffeomorphisms gives such a reducibility transformation. We give a concrete description of the ghost structure, and demonstrate that the infinite sums give the correct (regularised) number of degrees of freedom. The ghost towers belong to the sequences of representations previously observed appearing in tensor hierarchies and Borcherds algebras. All calculations rely on the section condition, which we reformulate as a linear condition on the cotangent directions. The analysis holds for n < 8. At n = 8, where the dual gravity field becomes relevant, the natural guess for the gauge parameter and its reducibility still yields the correct counting of gauge parameters.

The structure of maximally supersymmetric Yang-Mills theory: constraining higher-order corrections

We solve the superspace Bianchi identities for ten-dimensional supersymmetric Yang-Mills theory without imposing any kind of constraints apart from the standard conventional one. In this way we obtain a set of algebraic conditions on certain fields which in the on-shell theory are constructed as composite ones out of the physical fields. These conditions must hence be satisfied by any kind of theory in ten dimensions invariant under supersymmetry and some, abelian or non-abelian, gauge symmetry. Deformations of the ordinary SYM theory (as well as the fields) are identified as elements of a certain spinorial cohomology, giving control over field redefinitions and the distinction between physically relevant higher-order corrections and those removable by field redefinitions. The conditions derived severely constrain theories involving F2-level terms plus higher-order corrections, as for instance those derived from open strings as effective gauge theories on D-branes.

Particles, twistors and the division algebras

We study twistorial mechanics of particles and super-particles in six dimensions. To this end we formulate (in a general division algebra framework) a twistor theory in D = 6 based on quaternionic numbers, and prove the equivalence between this version of particle dynamics and the ordinary one. The super-twistors define a covariant and gauge invariant concept of a super world-line and allow us to write an action for the supersymmetric particle that is not plagued by the content of second class constraints that prevents a covariant quantization in the space-time picture. The notion and geometry of projectile twistor space, and its connection to Minkowski space, are examined and shown to directly generalize the results in D = 3, 4. Quantization is performed and analytic quaternionic eigenfunctions and integrations are discussed. We also draw some conclusions on the possible generalization to ten dimensions.

Exceptional geometry and tensor fields

A bstractWe present a tensor calculus for exceptional generalised geometry. Expressions for connections, torsion and curvature are given a unified formulation for different exceptional groups En(n). We then consider “tensor gauge fields” coupled to the exceptional generalised gravity. Many of the properties of forms on manifolds are carried over to these fields.

Global aspects of double geometry

A bstractWe consider the concept of a generalised manifold in the O(d, d) setting, i.e., in double geometry. The conjecture by Hohm and Zwiebach for the form of finite generalised diffeomorphisms is shown to hold. Transition functions on overlaps are defined. Triple overlaps are trivial concerning their action on coordinates, but non-trivial on fields, including the generalised metric. A generalised manifold is an ordinary manifold, but the generalised metric on the manifold carries a gerbe structure. We show how the abelian behaviour of the gerbe is embedded in the non-abelian T-duality group. We also comment on possibilities and difficulties in the U-duality setting.

Manifestly supersymmetric M-theory

In this paper, the low-energy effective dynamics of M-theory, eleven-dimensional supergravity, is taken off-shell in a manifestly supersymmetric formulation. We show that a previously proposed relaxation of the superspace torsion constraints does indeed accommodate a current supermultiplet which lifts the equations of motion corresponding to the ordinary second order derivative supergravity lagrangian. We comment on the relation and application of this completely general formalism to higher-derivative (R4) corrections. Some details of the calculation are saved for a later publication.

The manifestly Sl(2,Z)-covariant superstring

We present a manifestly Sl(2;Z)-covariant action for the type IIB superstring, and prove kappa-symmetry for on-shell IIB supergravity backgrounds.

An action for the superfive-brane in D=11 supergravity

An alternative path is taken for deriving an action for the supersymmetric 5- brane in 11 dimensions. Selfduality does not follow from the action, but is consistent with the equations of motion for arbitrary supergravity backgrounds. The action involves a 2-form as well as a 5-form world-volume potential; inclusion of the latter makes the action, as well as the non-linear selfduality relation for the 3-form eld strength, polyno- mial. The requirement of invariance under -transformations determines the form of the selfduality relation, as well as the action. The formulation is shown to be equivalent to earlier formulations of 5-brane dynamics.