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

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

Basic JCL for the CRAY-1 operating system (COS) with emphasis on making the transition from CDC 7600/SCOPE

Users of the CDC 7600 at Ames are assisted in making the transition to the CRAY-1. Similarities and differences in the basic JCL are summarized, and a dozen or so examples of typical batch jobs for the two systems are shown in parallel. Some changes to look for in FORTRAN programs and in the use of UPDATE are also indicated. No attempt is made to cover magnetic tape handling. The material here should not be considered a substitute for reading the more conventional manuals or the User's Guide for the Advanced Computational Facility, available from the Computer Information Center

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

Invariants and divergences in half-maximal supergravity theories

The invariants in half-maximal supergravity theories in D=4,5 are discussed in detail up to dimension eight (e.g. R^4). In D=4, owing to the anomaly in the rigid SL(2,R) duality symmetry, the restrictions on divergences need careful treatment. In pure N=4 supergravity, this anomalous symmetry still implies duality invariance of candidate counterterms at three loops. Provided one makes the additional assumption that there exists a full 16-supercharge off-shell formulation of the theory, counterterms at L>1 loops would also have to be writable as full-superspace integrals. At the three-loop order such a duality-invariant full-superspace integral candidate counterterm exists, but its duality invariance is marginal in the sense that the full-superspace counter-Lagrangian is not itself duality-invariant. We show that such marginal invariants are not allowable as counterterms in a 16-supercharge off-shell formalism. It is not possible to draw the same conclusion when vector multiplets are present because of the appearance of F^4 terms in the SL(2,R) anomaly. In D=5 there is no one-loop anomaly in the shift invariance of the dilaton, and we argue that this implies finiteness at two loops, again subject to the assumption that 16 supercharges can be preserved off-shell.Comment: 81 page

(N,p,q) Harmonic Superspace

A family of harmonic superspaces associated with four-dimensional spacetime is described. Some applications to supersymmetric field theories, including supergravity, are given.Comment: 25 pages, latex file, improved. Minor text errors correcte

Robust active magnetic dearing control using stabilizing dynamical compensators

The robust control of active magnetic bearings, based on a linearised interval model, is considered. Through robust stability analysis, all the first-order robust stabilizing dynamical compensators for the interval system are obtained. Disturbance attenuation and minimum control effort are also addressed. The approach is applied to a high-speed flywheel supported by two active and two passive magnetic bearings. Simulation and experimental results both show that it is simple, effective, and robust

Finiteness and anomalies in (4,0) supersymmetric sigma models

Power-counting arguments based on extended superfields have been used to argue that two-dimensional supersymmetric sigma models with (4,0) supersymmetry are finite. This result is confirmed up to three loop order in pertubation theory by an explicit calculation using (1,0) superfields. In particular, it is shown that the finite counterterms which must be introduced into the theory in order to maintain (4,0) supersymmetry are precisely the terms that are required to establish ultra-violet finiteness.Comment: 19 page

Noncommutative symmetric functions and Laplace operators for classical Lie algebras

New systems of Laplace (Casimir) operators for the orthogonal and symplectic Lie algebras are constructed. The operators are expressed in terms of paths in graphs related to matrices formed by the generators of these Lie algebras with the use of some properties of the noncommutative symmetric functions associated with a matrix. The decomposition of the Sklyanin determinant into a product of quasi-determinants play the main role in the construction. Analogous decomposition for the quantum determinant provides an alternative proof of the known construction for the Lie algebra gl(N).Comment: 25 page