Given that every particle that we have experimental confirmation of is an oscillation of its field (from what we know), and given dark matter is thought to be a particle yet undiscovered according to most theory, isn't it implied that this is an oscillation in a yet unknown field? Especially with the lack of results relating to WIMPs and other particles theorized.
What theories predict a new field relating to dark matter? Have any garnered significant interest and additional work?
Based on the predictive and explanatory success of quantum field theory, a new dark matter particle is defined as an excitation in a new matter field. So the answer to "What theories predict a new field relating to dark matter?" is "all widespread theories of dark matter," because there is simply no reason not to assume that quantum field theory works.
Based on your comments, some clarification is necessary on the definition of a "force." The macroscopic, Newtonian definition of "force" is "an interaction that, in the absence of other interactions, would cause an object to accelerate." It's pretty clear that you can't apply this to QFT - for one thing, how many objects are present isn't even well-defined in most high-energy interactions! The definition of "force" in quantum field theory seems to be somewhat nebulous and may even be arbitrary: see the discussion here for details: What is the definition of "force" in quantum field theory?. So it's not clear that your question on whether this constitutes a "new force" is strictly answerable without also supplying your definition of "force."
In the standard model of particle physics the fundamental forces are carried by the gauge bosons of the $SU(3)xSU(2)xU(1)$ theory. In the Feynman diagrams, any $dp/dt$ transferred in the interaction can be considered as a force, but there are just three fundamental forces, weak, strong, electromagnetic (and in effective quantizations of gravity, also gravitational) .
For dark matter extensions of the standard model and completely new theories ( like string theory) may be used. For GUTS there are extra symmetries and extra gauge bosons,, sometimes called X and Y, in analogy with the weak W and Z so in this sense there are extra fundamental forces at that level.
At the moment it will depend on the models used in the case that WIMPs are the constituents of dark matter. There are other models for dark matter, like MACHOs that have nothing to do with fundamental forces.
