BPS States, Weight Spaces and Vanishing Cycles

We review some simple group theoretical properties of BPS states, in relation with the singular homology of level surfaces. Primary focus is on classical and quantum N=2 supersymmetric Yang-Mills theory, though the considerations can be applied to string theory as well.Comment: for Proceedings of ``Strings 95'', 12p, plain TeX, 6 uuencoded ps figure

Special Geometry and Mirror Symmetry for Open String Backgrounds with N=1 Supersymmetry

We review an approach for computing non-perturbative, exact superpotentials for Type II strings compactified on Calabi-Yau manifolds, with extra fluxes and D-branes on top. The method is based on an open string generalization of mirror symmetry, and takes care of the relevant sphere and disk instanton contributions. We formulate a framework based on relative (co)homology that uniformly treats the flux and brane sectors on a similar footing. However, one important difference is that the brane induced potentials are of much larger functional diversity than the flux induced ones, which have a hidden N=2 structure and depend only on the bulk geometry. This introductory lecture is meant for an audience unfamiliar with mirror symmetry.Comment: latex, 35p, 2 figs, refs added; brief comments about duality to fourfolds added in the concluding sectio

Recent Developments in String Theory

After briefly reviewing basic concepts of perturbative string theory, we explain in simple terms some of the new findings that created excitement among the string physicists. These developments include non-perturbative dualities and a unified picture that embraces the so-far known theories. (An overview for non-experts)Comment: 16 p, latex, lprocl.sty, 12 figs, Contribution to the Proceedings of Lepton-Photon 97. Continuous updates at http://nxth21.cern.ch/~lerche/papers/strings.ps.g

On the Heterotic/F-Theory Duality in Eight Dimensions

We review quantitative tests on the duality between the heterotic string on T^2 and F-theory on K3. On the heterotic side, certain threshold corrections to the effective action can be exactly computed at one-loop order, and the issue is to reproduce these from geometric quantities pertaining to the K3 surface. In doing so we learn about certain non-perturbative interactions of 7-branes.Comment: latex, 10 figs, contribution to the proceedings of Cargese 199

Chiral Rings in Topological (W-)Gravity

Talk given at the 26th Workshop: ``From Superstrings to Supergravity", Erice - Sicily, 5-12 December 1992. We review the superconformal properties of 2d matter coupled to gravity, and extensions thereof. Focusing on topological strings, we recall how the superconformal structure helps to provide a direct link between Liouville theory coupled to matter, and matrix models. We also construct an infinite class of new theories based on $W$-gravity.Comment: 13pages, plain te

The Unfree Labour Category and Unfree Labour Estimates: A Continuum within Low-End Labour Relations

The article argues against the singling out of unfree labour as something wholly unique and entirely separate and different from other labour relations. Existing dichotomous approaches to free–unfree labour hinder a proper understanding of these labour relations, both theoretically and empirically. It argues that the way in which both mainstream and Marxist approaches conceptualise and operationalise unfree/forced labour is problematic and proposes replacing the unfree-free dichotomy with a continuum of unfreedoms. Such unfreedoms should be understood as one among many ‘un-decent’ forms and aspects of labour relations. All of these can be understood as outcomes of the class struggle from above, which in today’s world is part and parcel of neo-liberalism. The discussion is informed by examples primarily from India and China

Non-Abelian Born-Infeld Action and Type I - Heterotic Duality (II): Nonrenormalization Theorems

Type I - heterotic duality in D=10 predicts various relations and constraints on higher order F^n couplings at different string loop levels on both sides. We prove the vanishing of two-loop corrections to the heterotic F^4 terms, which is one of the basic predictions from this duality. Furthermore, we show that the heterotic F^5 and (CP even) F^6 couplings are not renormalized at one loop. These results strengthen the conjecture that in D=10 any Tr F^(2n) coupling appears only at the disc tree-level on type I side and at (n-1)-loop level on the heterotic side. Our non-renormalization theorems are valid in any heterotic string vacuum with sixteen supercharges.Comment: 35 pages, harvmac; cosmetic changes; final version to appear in NP

An Equilibrium State for the Interstellar Gas and Magnetic Field

Equilibrium state for interstellar gas and magnetic fiel