Introduction to string theory: its structure and its uses

Abstract

Over five years ago experiments at CERN confirmed that the weak (radioactive) interactions of elementary particles are mediated by gauge particles that are heavy relatives of the photon, namely the quantum of light and radio wave propagation. Gauge particles have to belong to a pattern given by the structure of a compact Lie group. Mathematicians listed such patterns at the beginning of the century and it seems that nature favours one of the ‘exceptional’ possibilities when nuclear forces are included. Twenty years ago a picture of elementary particles as quanturns of the excitations of a one-dimensional string was developed. Consistency with the principles of relativity and quantum mechanics seemed to require the aforementioned exceptional gauge structure as well as gravitational forces in Einstein’s formulation. Thus a simple ‘string’ principle promised to explain and unify all the diverse fundamental forces of nature: electromagnetic, weak, nuclear and gravitational. Unfortunately, there remain detailed questions still to be resolved. Nevertheless, the theory possesses rich mathematical structure encompassing Lie algebras and infinite-dimensional generalizations and complex algebraic geometry in a way which sheds valuable new perspectives on modern pure mathematics. At the same time it has unexpected applications in describing and classifying the modes of phase transition in two-dimensional materials, a classical problem in statistical physics.