KK Compactification of Supergravity Models

Abstract

In this chapter, we will study the KK compactification of supergravity models in higher dimensions. Supergravity models in higher dimensions have: -a graviton, described by the metric gμν (which can be written as eμaηabeνb ), except for the coupling to fermions, which is written in terms of ωμab(e). -gravitino(s) (Figure presented.) ψμαi, one for each supersymmetry. Indeed, each supersymmetry ϵi takes us from the graviton to a different gravitino, δeμa=ϵ¯iγaψμi. -other fields: scalars ϕI, vectors AμI, spinors λαI, and also antisymmetric tensors Aμ1..μr. The antisymmetric tensors are generalizations of the gauge fields (Maxwell fields) Aμ, that have also a field strength, (Formula Presented), and so satisfy a gauge invariance (Formula Presented). The gauge invariant action for the antisymmetric tensor field is (Formula Presented).