Chiral deformations of Yang-Mills and Gravity theories

In this thesis we present a modification of Yang-Mills and Gravity theories both written in terms of gauge connections. In particular gravity is presented in its pure connection formulation realizing a Diffeomorphism Invariant Gauge Theory. The modifications do not change the kinematical content of the theories, but they add an infinite set of new vertices retaining the symmetries of the original Lagrangians without introducing higher derivatives in the equations of motion. These new interactions are chiral, leaving the original Yang Mills and Gravity theories as the only parity-invariant theories in the set. In the Yang-Mills case we proved that at tree level the theory is still constructible via the so-called BCFW recursion relations. Both theories are claimed to be closed under the renormalization group. The Yang-Mills Deformations are indeed proved to be one-loop renormalizable and an explicit diagrammatic computation of the simplest deformation beta-function is given. For gravity a new formulation is introduced that could lead to a similar result at one-loop