Yes, one example of a field theory that has been experimentally proven to be true is the Standard Model of particle physics. The Standard Model is a quantum field theory that describes the fundamental particles and their interactions through three fundamental forces: the electromagnetic force, the weak force, and the strong force (described by quantum electrodynamics, electroweak theory, and quantum chromodynamics, respectively).
Experimental evidence from various particle accelerators and colliders, such as the Large Hadron Collider (LHC) at CERN, has provided strong confirmation of the predictions of the Standard Model. For example:
Discovery of the Higgs boson: The existence of the Higgs boson, a particle associated with the Higgs field, was predicted by the Standard Model. In 2012, experimental observations at the LHC confirmed the existence of the Higgs boson, providing a significant confirmation of the Standard Model.
Precision tests of electroweak theory: The predictions of the electroweak theory, which unifies the electromagnetic and weak forces, have been extensively tested and found to be in excellent agreement with experimental measurements. These tests include precision measurements of the properties of the W and Z bosons, as well as measurements of electroweak processes at various energies.
QCD and strong force: Quantum chromodynamics (QCD), the quantum field theory that describes the strong force, has been extensively tested in various experiments. These tests include measurements of the properties of hadrons (particles composed of quarks), the observation of quark-gluon plasma in high-energy collisions, and studies of jets and other phenomena involving the strong force.
While the Standard Model has been highly successful in describing a wide range of particle physics phenomena, it is known to be incomplete and does not incorporate gravity. The quest for a more comprehensive theory, such as a theory of quantum gravity, remains an active area of research in theoretical physics.