In this chapter we consider different aspects of the low-energy 4d effective action of heterotic compactifications. After discussing the structure of the effective action for the general CY compactifications of Chapter 7, we concentrate on the case of the abelian orbifold compactifications of Chapter 8, in which several additional aspects can be described in an explicit quantitative fashion. We discuss the form of the Kähler potential and the superpotential, as well as the gauge kinetic function and their one-loop corrections. In toroidal orbifolds the low-energy effective actionmust bemodular invariant under T-duality transformations, and this leads to strong constraints on its structure. A general feature of heterotic compactifications is that they often have a non-trivial cancellation of mixed U(1) anomalies, involving a generalized Green×Schwarz mechanism. This renders some U(1) gauge bosons massive, and introduces a one-loop re-stabilization of the vacuum, triggering the breaking of extra gauge symmetries and the disappearance of charged matter multiplets. This phenomenon can be efficiently exploited in the construction of improved models of particle physics, as we describe using explicit examples.

A first look at the heterotic 4d N =1 effective action

We start by motivating the general structure of the effective action of heterotic string geometric (CY or orbifold) compactifications by using an intuitive description of the truncation to the zero mode sector. The resulting structure is quite general, as can be shown to largely follow from symmetries of the system. We finally describe more explicit results for CY compactifications with standard embedding.