M Theory Fivebrane and SQCD

In this note we provide a new perspective on the topological parts of several action functionals in string and M-theory. We show that rationally these can be viewed as large gauge transformations corresponding to variations of higher structures, such as String, Fivebrane, and Ninebrane structures.

Is large-$N$ QCD equivalent to a string theory? Maybe, maybe not. I review various attempts to answer the question.

We relate Type IIB superstrings compactified to six dimensions on K3 to an eleven-dimensional theory compactified on $({\bf S}^1)^5/{\bf Z}_2$. Eleven-dimensional five-branes enter the story in an interesting way.

We review the structure and symmetry properties of the worldvolume action for the M-theory 5-brane and of its equations of motion.

Talk given at ICM '98, Berlin, reviewing some of the recent developments in understanding of string theory for a mathematical audience (to appear in Documenta Mathematica).

We review the relation between the classical dynamics of the M-fivebrane and the quantum low energy effective action for N=2 Yang-Mills theories. We also discuss some outstanding issues in this correspondence.

The dynamics of a probe M5-brane, embedded as a hypersurface in eleven-dimensional Minkowski spacetime, is described by a six-dimensional world-volume theory. This theory has a variety of interesting symmetries some of which are obscure in the Lagrangian formulation of the theory. However, as summarized in this review, an alternative approach is to construct all of its on-shell tree-level scattering amplitudes. This enables understanding all of the symmetries in a satisfying ...

This is a non-technical talk given at the Sixth Marcel Grossman Meeting on General Relativity, Kyoto, Japan in June 1991. Some developments in string theory over the last six years are discussed together with their qualitative implications for issues in quantum gravity.

Lectures presented at the Spring School, Trieste, Italy 1993.

This is a talk delivered at the Meeting on Integrable Quantum Field Theories, Villa Olmo and at STRINGS 1992, Rome, September 1992. I discuss some recent attempts to revive two old ideas regarding an analytic approach to QCD-the development of a string representation of the theory and the large N limit of QCD.