Diffeomorphism invariant gauge theories - Torres Gomez, Alexander (2012)
A class of diffeomorphism invariant gauge theories is studied. The action for this class of theories can be formulated as a generalisation of the well known topological BF-theories with a potential for the B-field or in a pure connection formulation. When the gauge group is chosen to be SU(2) the theory describes gravity. For a larger gauge group G one gets a unified model of gravity and Yang-Mills fields. A background for the theory is chosen which breaks the gauge group G by selecting in it a preferred SU(2) subgroup which describes the gravitational sector. The Yang-Mills sector is described by the part of the gauge group that commutes with this SU(2). Thus, when the action is expanded around this background the spectrum of the linearised theory consists of the usual gravitons plus Yang-Mills fields. In addition, there is a set of massive scalar fields that are charged both under the gravitational and Yang-Mills subgroups. The latter sector is described by the part of the gauge group that does not commute with SU(2). A fermionic Lagrangian is also proposed which can be coupled to the BF plus potential formulation.