Sigma models with off-shell N=(4,4) supersymmetry and noncommuting complex structures

We describe the conditions for extra supersymmetry in N=(2,2) supersymmetric nonlinear sigma models written in terms of semichiral superfields. We find that some of these models have additional off-shell supersymmetry. The (4,4) supersymmetry introduces geometrical structures on the target-space which are conveniently described in terms of Yano f-structures and Magri-Morosi concomitants. On-shell, we relate the new structures to the known bi-hypercomplex structures.Comment: 20 pages; v2: significant corrections, clarifications, and reorganization; v3: discussion of supersymmetry vs twisted supersymmetry added, relevant signs corrected

Palatini Variational Principle for NN-Dimensional Dilaton Gravity

We consider a Palatini variation on a general $N$-Dimensional second order, torsion-free dilaton gravity action and determine the resulting equations of motion. Consistency is checked by considering the restraint imposed due to invariance of the matter action under simple coordinate transformations, and the special case of N=2 is examined. We also examine a sub-class of theories whereby a Palatini variation dynamically coincides with that of the "ordinary" Hilbert variational principle; in particular we examine a generalized Brans-Dicke theory and the associated role of conformal transformations.Comment: 16 pages, LaTe

Space-Time Symmetries of Quantized Tensionless Strings

The tensionless limit of the free bosonic string is space-time conformally symmetric classically. Requiring invariance of the quantum theory in the light cone gauge tests the reparametrization symmetry needed to fix this gauge. The full conformal symmetry gives stronger constraints than the Poincar\'e subalgebra. We find that the symmetry may be preserved in any space-time dimension, but only if the spectrum is drastically reduced (part of this reduction is natural in a zero tension limit of the ordinary string spectrum). The quantum states are required to be symmetric ({\it i.e.} singlets) under space-time diffeomorphisms, except for the centre of mass wave function.Comment: 15pp, plain latex, USITP-92-

Properties of hyperkahler manifolds and their twistor spaces

We describe the relation between supersymmetric sigma-models on hyperkahler manifolds, projective superspace, and twistor space. We review the essential aspects and present a coherent picture with a number of new results.Comment: 26 pages. v2: Sign mistakes corrected; Kahler potential explicitly calculated in example; references added. v3: Published version--several small clarifications per referee's reques

The Semi-Chiral Quotient, Hyperkahler Manifolds and T-duality

We study the construction of generalized Kahler manifolds, described purely in terms of N=(2,2) semichiral superfields, by a quotient using the semichiral vector multiplet. Despite the presence of a b-field in these models, we show that the quotient of a hyperkahler manifold is hyperkahler, as in the usual hyperkahler quotient. Thus, quotient manifolds with torsion cannot be constructed by this method. Nonetheless, this method does give a new description of hyperkahler manifolds in terms of two-dimensional N=(2,2) gauged non-linear sigma models involving semichiral superfields and the semichiral vector multiplet. We give two examples: Eguchi-Hanson and Taub-NUT. By T-duality, this gives new gauged linear sigma models describing the T-dual of Eguchi-Hanson and NS5-branes. We also clarify some aspects of T-duality relating these models to N=(4,4) models for chiral/twisted-chiral fields and comment briefly on more general quotients that can give rise to torsion and give an example.Comment: 31 page

ADE-Quiver Theories and Mirror Symmetry

We show that the Higgs branch of a four-dimensional Yang-Mills theory, with gauge and matter content summarised by an ADE quiver diagram, is identical to the generalised Coulomb branch of a four-dimensional superconformal strongly coupled gauge theory with ADE global symmetry. This equivalence suggests the existence of a mirror symmetry between the quiver theories and the strongly coupled theories.Comment: 8 pages, 4 figures. Talk delivered by UL at D.V. Volkov Memorial Conference, July 25-29, 2000, Kharkov, to be published in the proceeding

Generalized Kahler Geometry from supersymmetric sigma models

We give a physical derivation of generalized Kahler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri regarding the equivalence between generalized Kahler geometry and the bi-hermitean geometry of Gates-Hull-Rocek. When cast in the language of supersymmetric sigma models, this relation maps precisely to that between the Lagrangian and the Hamiltonian formalisms. We also discuss topological twist in this context.Comment: 18 page

Evaluation of animal and veterinary science teaching at the University of Nairobi

Sixty-two students, graduating in 1975 from the Faculty of Veterinary Medicine, University of Nairobi, Kenya, were sent a questionnaire, which was returned by 41. The graduates scored 4 aspects of the teaching in each subject on a scale from 1 = very poor to 5 = very good. The overall average for all years was 3.51 ± .45, indicating that the teaching was regarded as satisfactory, but not as particularly good. The variation between subjects was large, the poorest subject getting an average score of 2.78 ± .78 and the best a score of 3.94 ± .68, the coefficient of variation ranging from 14 to 28. In many subjects the practical instruction was rated much lower than the theoretical one, and in one case the difference was as large as 1.61 points. The use and quality of teaching material was generally rated lower than theoretical instruction, as were examinations. These results, as well as the comments provided by the students indicate that there is considerable scope for improvement of the teaching in many subjects

Selection intensity for milk yield in 1970—1977 in the Finnish Ayrshire

Selection differentials for sires and dams of bulls taken into AI use in 1970—1977, as well as for sires used in AI, were combined with an estimate of the quality of dams of female replacements to calculate the (predicted) genetic change in milk yield in the Ayrshire breed. In the period the average annual genetic gain was 0.97 % of the mean yield, in the last three years it was c. 1.1 %. The average generation interval was 6.8 years; 8.7 years for the bull sires, 7.4 years for the bull dams and 6.4 years for the cow sires. The bull sires accounted for 42 %, the bull dams for 37 % and the cow sires for only 12% of the total genetic gain. A more rational use of progeny tested and young bulls, combined with a reduction of the generation interval of 15 %, could easily have increased the genetic progress by 20 %

Generalized Kahler geometry and gerbes

We introduce and study the notion of a biholomorphic gerbe with connection. The biholomorphic gerbe provides a natural geometrical framework for generalized Kahler geometry in a manner analogous to the way a holomorphic line bundle is related to Kahler geometry. The relation between the gerbe and the generalized Kahler potential is discussed.Comment: 28 page