Matrix models of 2d gravity

These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date. 0. Canned Diatribe, Introduction, and Apologies 1. Discretized surfaces, matrix models, and the continuum limit 2. All genus partition functions 3. KdV equations and other models 4. Quick tour of Liouville theoryComment: Trieste Lectures (July, 1991), 40p

Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation

It is shown that the Ginsparg-Wilson relation implies an exact symmetry of the fermion action, which may be regarded as a lattice form of an infinitesimal chiral rotation. Using this result it is straightforward to construct lattice Yukawa models with unbroken flavour and chiral symmetries and no doubling of the fermion spectrum. A contradiction with the Nielsen-Ninomiya theorem is avoided, because the chiral symmetry is realized in a different way than has been assumed when proving the theorem.Comment: plain tex source, 8 pages, no figure

Exact Supersymmetry on the Lattice

We discuss the possibility of representing supersymmetry exactly in a lattice discretized system. In particular, we construct a perfect supersymmetric action for the Wess-Zumino model.Comment: 9 pages, LaTex, no figure

Desperately Seeking Superstrings

We provide a detailed analysis of the problems and prospects of superstring theory c. 1986, anticipating much of the progress of the decades to follow.Comment: originally appeared as a Reference Frame in Physics Today, May 198

More about exactly massless quarks on the lattice

In a previous publication [hep-lat/9707022] I showed that the fermion determinant for strictly massless quarks can be written on the lattice as $\det D$, where $D$ is a certain finite square matrix explicitly constructed from the lattice gauge fields. Here I show that $D$ obeys the Ginsparg-Wilson relation $D\gamma_5 D = D\gamma_5 +\gamma_5 D$.Comment: 4 pages, plain Te