Gauge field corrections to 11-dimensional supergravity via dimensional reduction

Using the fact that eleven-dimensional supergravity yields type IIA supergravity under dimensional reduction on a circle, we determine higher-derivative terms of 11-dimensional supergravity including the \( R^4 \), \( ({\partial {F_4}})^2 R^2 \) and \( ({\partial {F_4}})^4 \) terms.