CALT-68-2065\
hep-th/9607201

= 20pt

Lectures on Superstring and M Theory Dualities[^1]

John H. Schwarz\
*California Institute of Technology, Pasadena, CA 91125, USA*

**Abstract**

> These lectures begin by reviewing the evidence for S duality of the toroidally compactified heterotic string in 4d that was obtained in the period 1992–94. Next they review recently discovered dualities that relate all five of the 10d superstring theories and a quantum extension of 11d supergravity called M theory. The study of $p$-branes of various dimensions (some of which are $D$-branes) plays a central role. The final sections survey supersymmetric string vacua in 6d and some of the dual constructions by which they can be obtained. Special emphasis is given to a class of $N=1$ models that exhibit “heterotic-heterotic duality.”

*Lectures presented at the ICTP Spring School (March 1996)*

*and at the TASI Summer School (June 1996)*

Introduction
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In the first superstring revolution (1984–85) we learned that there are just five superstring theories, each of which admits a 10d Poincaré-invariant vacuum and has a perturbation expansion that is consistent at every finite order.[@green87] Three of the theories have $N=1$ supersymmetry in 10d (type I and the two heterotic theories), one has $N=2$ supersymmetry in 