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

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

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

A Calibration Bound for the M-Theory Fivebrane

We construct a covariant bound on the energy-momentum of the M-fivebrane which is saturated by all supersymmetric configurations. This leads to a generalised notion of a calibrated geometry for M-fivebranes when the worldvolume gauge field is non-zero. The generalisation relevant for Dp-branes is also given.Comment: 9 pages, LaTeX2e, uses vmargin.sty. Typos corrected, a reference and a new discussion on conserved charges added. v4: A typo in the expression for the D-fourbrane energy correcte

Teaching Language to Students with Autism

This meta-synthesis of the literature on methods of instruction to students with ASD examines the various methods of teaching language to students with ASD. While each student learns language at his or her own pace, the author has found that certain methods yield results quicker, and these methods need to be examined critically for any literature on their reliability, efficacy, and scientific research. If a student with autism can be taught language quickly, therefore mitigating any further delays in academic development relative to peers, then this methodology should be made accessible to all teachers of such students

The strain energy analysis of swept boxes with ribs normal to the spars

The root constraint problem associated with uniform rectangular swept boxes, having ribs normal to the spars is considered. A strain energy method using self-equilibrating internal end load systems is used. Continues

On the Energy Momentum Tensor of the M-Theory Fivebrane

We construct the energy momentum tensor for the bosonic fields of the covariant formulation of the M-theory fivebrane within that formalism. We then obtain the energy for various solitonic solutions of the fivebrane equations of motion.Comment: 12 pages, LaTeX2e, uses vmargin.sty and amstex.st