Lectures on Heterotic String and Orbifold Compactifications

Abstract

These lectures are concerned with the structure of the heterotic string and with special soluble compactifications of string theory. The first lecture discusses the connection between anomaly cancellation in the low-energy limit of consistent strings and the chiral current algebra structure of the heterotic string. The second lecture gives a brief introduction to toroidal and orbifold compactifications in string theory. The third lecture is based on work done in collaboration with G.Moore and C.Vafa and concerns “quasicrystalline” orbifold compactifications. These compactifications exhibit symmetries related to those of quasicrystals at irrational values of the background fields. They are most naturally formulated using certain ideas from number theory.