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

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

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

A note on the UV behaviour of maximally supersymmetric Yang-Mills theories

The question of whether BPS invariants are protected in maximally supersymmetric Yang-Mills theories is investigated from the point of view of algebraic renormalisation theory. The protected invariants are those whose cohomology type differs from that of the action. It is confirmed that one-half BPS invariants ($F^4$) are indeed protected while the double-trace one-quarter BPS invariant ($d^2F^4$) is not protected at two loops in D=7, but is protected at three loops in D=6 in agreement with recent calculations. Non-BPS invariants, i.e. full superspace integrals, are also shown to be unprotected.Comment: 12 pages. Minor changes to text. References adde

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

Supersymmetry counterterms revisited

Superspace power-counting rules give estimates for the loop order at which divergences can first appear in non-renormalisable supersymmetric field theories. In some cases these estimates can be improved if harmonic superspace, rather than ordinary superspace, is used. The new estimates are in agreement with recent results derived from unitarity calculations for maximally supersymmetric Yang-Mills theories in five and six dimensions. For N=8 supergravity in four dimensions, we speculate that the onset of divergences may correspondingly occur at the six loop order.Comment: 10 pages, plain Late

Quantizing the (0,4) Supersymmetric ADHM Sigma Model

We discuss the quantization of the ADHM sigma model. We show that the only quantum contributions to the effective theory come from the chiral anomalies and compute the first and second order terms. Finally the limit of vanishing instanton size is discussed.Comment: 19 pages phyzzx. Expanded discussion of various point and some minor correction

Monopole Dynamics from the M-Fivebrane

We study the BPS states of the M-fivebrane which correspond to monopoles of N=2 SU(2) gauge theory. Far away from the centres of the monopoles these states may be viewed as solitons in the Seiberg-Witten effective action. It is argued that these solutions are smooth and some properties of their moduli space are discussed.Comment: 30 pages phyzzx. Paragraph added to the introduction and some minor corrections. To appear in Nucl. Phys.

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

Brane Rotating Symmetries and the Fivebrane Equations of Motion

We show that the fully covariant equations of motion for the M-theory fivebrane can be interpreted as charge conservation equations. The associated charges induce `shift'-symmetries of the scalar, spinor and gauge-fields of the fivebrane, so allowing an interpretation of all these fields as Goldstone fields. We also find that the fivebrane possesses a new symmetry that is part of the GL(32) automorphism group of the eleven dimensional supersymmetry algebra.Comment: 15 pages, late