Toroidal compactification of superstrings
In this chapter we study the toroidal compactification of superstrings. The main motivation is to produce 4d theories at low energies, as a preliminary tool for toroidal orbifold constructions, and as a warm-up for more involved Calabi–Yau compactifications. Toroidal compactifications also frame interesting T-dualities among different superstring theories. We mostly focus on circle compactification of one dimension, which generalizes easily to compactifications to 4d.
5.1 Type II superstrings
We start with the circle compactification of type II theories, and the T-duality relation between type IIB and IIA compactifications.
5.1.1 Circle compactification
Consider type IIA or IIB theories compactified ...