8 - Perturbative Descriptions of Gravity

Summary

are considered: chiral Einstein-Cartan, and chiral pure connection one. It is explained why chiral 4D perturbative formalisms are particularly powerful - they work with the minimal possible number of auxiliary fields to achieve polynomiality of the action. Spinors and differential operators that are motivated by spinors play a particularly important role in this Chapter, and so Lorentzian signature spinors are reviewed here in some detail. We also treat Yang-Mills theory and show how its chiral first order formalism gives the most powerful perturbative description. We end by describing how to gauge-fix the pure connection action on an arbitrary Einstein background. This produces a very simple perturbative description, remarkably more economic than the usual metric one.