The Six Dimensional Self-Dual Tensor

The equations of motion for a self-interacting self-dual tensor in six dimensions are extracted from the equations describing the M-theory five-brane. These equations are presented in a self-contained, six-dimensional Lorentz-covariant form. In particular, it is shown that the field-strength tensor satisfies a non-linear generalised self-duality constraint. The self-duality equation is rewritten in five-dimensional notation and shown to be identical to the corresponding equation in the non-covariant formalism.Comment: 8 pages, late

3-Point Functions in N=4 Yang-Mills

Three-point functions of analytic (chiral primary) operators in N=4 Yang-Mills theory in four dimensions are calculated using the harmonic superspace formulation of this theory. In the case of the energy-momentum tensor multiplet anomaly considerations determine the coefficient. Analyticity in N=2 harmonic superspace is explicitly checked in a two-loop calculation.Comment: This file requires the feynman.tex macro Some references are adde

Nilpotent invariants in N=4 SYM

It is shown that there are no nilpotent invariants in N=4 analytic superspace for $n\leq4$ points. It is argued that there is (at least) one such invariant for n=5 points which is not invariant under U(1)_Y. The consequences of these results are that the n=2 and 3 point correlation functions of the N=4 gauge-invariant operators which correspond to KK multiplets in AdS supergravity are given exactly by their tree level expressions, the 4 point correlation functions of such operators are invariant under U(1)_Y and correlation functions with $n\geq 4$ points have non-trivial dependence on the Yang-Mills coupling constant.Comment: 9 page

Free Fermions and Extended Conformal Algebras

A class of algebras is constructed using free fermions and the invariant antisymmetric tensors associated with irreducible holonomy groups. (This version contains minor typographical corrections and some additional references. )Comment: 7 pages, KCL-Th-94-1

Strings and D-Branes with Boundaries

The covariant field equations of ten-dimensional super D-branes are obtained by considering fundamental strings whose ends lie in the superworldsurface of the D-brane. By considering in a similar fashion Dp-branes ending on D(p+2)-branes we derive equations describing D-branes with dual potentials, as well as the vector potentials.Comment: 12 pages, Late

On superembedding approach to type IIB 7-branes

In search for a dynamical description of Q7-branes, which were known as solutions of supergravity equations and then conjectured to be dynamical objects of type IIB string theory, we study the superembedding description of 7-branes in curved type IIB supergravity superspace. With quite minimal and natural assumptions we have found that there is no place for Q7-branes as dynamical branes in superembedding approach. Our study might give implications for the old-standing problem of the covariant and supersymmetric description of multiple Dp-brane systems.Comment: LaTeX, 40 pages, no figures. V2: 44 pages, misprints corrected, minor cosmetic changes, improvements and extensions of discussion, in particular in the parts devoted to derivation of D7-brane equations of motion (Sec. 3) and in Secs. 4.2; appendices E,F added, footnote on page 30 extended, conclusions remain the same. V3. More misprints correcte

Kappa-symmetric SL(2,R) covariant D-brane actions

A superspace formulation of IIB supergravity which includes the field strengths of the duals of the usual physical one, three and five-form field strengths as well as the eleven-form field strength is given. The superembedding formalism is used to construct kappa-symmetric SL(2,R) covariant D-brane actions in an arbitrary supergravity background.Comment: 20 pages. Minor clarification in text. References adde

Superconformal Invariants and Extended Supersymmetry

The superconformal invariants in analytic superspace are found. Superconformal invariance is shown to imply that the Green's functions of analytic operators are invariant holomorphic sections of a line bundle on a product of certain harmonic superspaces. It is argued that the correlation functions for a class of sufficiently low dimension gauge invariant operators in N=2 and N=4 supersymmetric Yang-Mills theory can be evaluated up to constants.Comment: 10p, late

Operator product expansions in four-dimensional superconformal field theories

The operator product expansion in four-dimensional superconformal field theory is discussed. The OPE takes a particularly simple form for chiral operators, in $N=1$ and $N=2$, and for analytic operators, in $N=2$ and $N=4$. It is argued that the Green's functions of such operators can be determined up to constants.Comment: 9 pages, late

Twistor spaces for HKT manifolds

We construct the twistor space associated with an HKT manifold, that is, a hyper-K\"ahler manifold with torsion, a type of geometry that arises as the target space geometry in two-dimensional sigma models with (4,0) supersymmetry. We show that this twistor space has a natural complex structure and is a holomorphic fibre bundle over the complex projective line with fibre the associated HKT manifold. We also show how the metric and torsion of the HKT manifold can be determined from data on the twistor space by a reconstruction theorem. We give a geometric description of the sigma model (4,0) superfields as holomorphic maps (suitably understood) from a twistorial extension of (4,0) superspace (harmonic superspace) into the twistor space of the sigma model target manifold and write an action for the sigma model in terms of these (4,0) superfields.Comment: 15 pages, Phyzz