M-Theory and N = 2 Strings

Abstract

A few years ago, if asked to describe string theory, the average practitioner would have classified its different manifestations according to their various worldsheet gauge principles. On the 1+1 dimensional worldsheet, there can be (p,q) super-symmetries that square to translations along the (left,right)-handed light cone; one says that the worldsheet has (p, q) gauged supersymmetry. The bosonic string has no supersymmetry; p = q = 0. The supersymmetric string theories have, say, q = 1. Thus type IIA/B string theory has (1,1) supersymmetry. The type I/IA strings are the orbifold of these by worldsheet parity, and the heterotic strings are in the class (0,1). Remarkably, we now understand that all the supersymmetric string theories — type IIA/B, type I, and heterotic — appear to describe asymptotic expansions of a single nonperturbative master theory: M-theory. This theory has many miraculous duality properties that are now only beginning to be unravelled; other lecturers at this school will review the current state of affairs. In these lectures, I will give an overview of a relatively unexplored corner of string theory, namely the N=2 strings [1, 2, 3] (more specifically strings with (2,2) or (2,1) gauged worldsheet supersymmetry).