Modave Lecture notes: Introduction to Exceptional Field Theory

Abstract

These notes are based on lectures given at the XIX Modave School on Mathematical Physics and present an introduction to Exceptional Field Theory. We cover the standard Kaluza-Klein reductions on tori, with applications to supergravity. We review the supergravity action of type IIA/IIB and eleven-dimensional supergravities. We motivate the appearance of the hidden symmetry groups ${\mathrm{E}}_{d(d)}$ through the lens of string dualities. We explore the construction and properties of ${\mathrm{E}}_{7(7)}$-ExFT and review other ${\mathrm{E}}_{d(d)}$-ExFT for $3\le d\le 8$, as well as double field theories. These notes conclude with some applications of ExFT to consistent truncations.

89 pages + references, 6 figures. Lecture notes from XIX Modave Summer School in Mathematical Physics, 2023