I always had the impression that physics depends a lot on particle accelerators and heavy machines for experimentation of new theories, I know there's the field called theoretical physics but until now I have no idea on how TF relies on these machines. Does theoretical physics rely a lot on this machinery?
There is no simple answer to this question. Physics, and the Natural Science, are basically based on the practice of distinguishing between hypotheses by empirical evidence, which implies experiments, so yes, in that sense we do need our equipment (and we need it well documented).
This is, however, not what you are asking, as I perceive it; what you want to know seems to be to what extent the large scale experiments are necessary.
The answer to this is that, yes, some branches of theoretical physics need large scale experiments if they are to be based in an empirical setting (which is what we desire, since this is how we evaluate scientific content).
The fields in question, cosmology and particle physics for instance, deal with questions of scales far removed from our everyday experience. In order to test the hypothesis of, for instance, the Higgs' boson, access to those scales is necessary, and for that case (and much of particle physics), the key obstacle that needs to be overcome is binding energy: the very small (hypothesised) building blocks of matter are very tightly bound (if they were not, the world we live in would not appear as solid to us, as it does), so in order to study them, we need large scale machines to break them apart.
Likewise, in astrophysics, larger (radio and other) telescopes allow us to probe deeper into the cosmos, which allows us to distinguish between more and more fundamental models of the early universe, for instance. (Incidentally, this brings us back to particle physics, but that is another story.)
Yes, physics is absolutely dependent on equipment which is needed so an observer can observe and register data so that they can be logically analyzed and the analysis used for predicting future behavior.
Actually there are many levels of instrumentation.
The first one is the observer's brain.
What we observe in nature exists in several scales and physics describes and makes predictions for all scales : from the distances of stars and galaxies and clusters of galaxies to the sizes of atoms and elementary particles.
Observing in human size scale means what our ears hear, what our eyes see, what our hands feel, our nose smells , our mouth tastes. That was the first classification and the level of "proxy", i.e. intermediate between fact and our understanding and classification, which is biological. (the term proxy is widely used in climate researches)
A second level of observing comes when we use proxies, like meters, thermometers, telescopes and microscopes etc. which register on our biological proxies and we accumulate knowledge. These are simple instruments, and with these instruments scientists gathered observations that were used by physicists to construct theories that would describe and predict further observations. At this level we overcome the limits of the human scale and find and study the enormous scales of the galaxies and the tiny scales of the bacteria and microbes. A level of microns and milimeters. We observe waves in liquids with such size wavelengths.
Presently we are studying experimentally dimensions that go from 10^-10 meters and smaller and have hit the basic building blocks of nature, the quantum mechanical level of nature. These experiments need accelerators and the theories describing the results and predicting new ones are at the frontier of physics . Theoretical physicists formulate mathematical models to this effect.
Yes theoretical physics does rely on the data given by large expensive accelerator experiments that need thousands of physicists and engineers to operate and analyze the results. Theoretical physics uses advanced mathematical methods but it is not enough to construct self consistent mathematical models. These models should be validated against the data in order to be called physics theoretical models.
Theoretical physics relies on experimental physics which relies on advanced experimental setups. Theoretical physics on its own is (in general) not any more demanding than mathematics. The help of computers is often needed for complex simulations, but you could argue that this is more computational physics.