1. QFT is generally accepted framework for describing strong, electromagnetic and weak interactions.
2. We can use gauge theories to describe all these three interactions. QED is abelian local U(1), QCD is local \(SU(3)_c\) and Weak interactions can be explained by invariance of physics under \(SU(2)\) local phase symmetry.
3. Electro-weak model (non Abelian \(SU(3)\times U(1)\)) (Glashow-Salam-Weinberg model) is spontaneously broken down to U(1) symmetry of electromagnetic interactions. Due to this breaking the mediators \(W^{\pm},Z_{0}\) becomes so massive implying short range for weak interactions.
4. The fundamental fermion(matter particle) which couple to vector bosons are quarks(u,d,c,s,t,b) and leptons(\(e^{-},\mu^{-1},\tau^{-1},\nu_{e},\nu_{\mu},\nu_{\tau}\)). The quarks can also change its flavour from up to down by emission of \(W^{+}\) boson. All quarks come in three colors and invariance of Lagrangian/physics under unbroken non abelian \(SU(3)_{color}\) describes QCD. It has total of \(3^2-1=8\) generators(massless(unbroken) gluons) to mediate interactions.
5. QCD is asymptotically free theory which means that for high energy or small separations the interactions strength becomes very small. This is an consequence of non abelian nature of local SU(3) symmetry. For larger separations of quarks the gluons (mediators) begin to interact with each other with larger interactions strength and thus confines quarks. Confinement is non perturbative phenomena and we have yet to prove mathematically that QCD confines quarks in low energy limit.
6. Once lattice formulation is proposed by K.G. Wilson in 1974 to probe non perturbative phenomena, we can now begin to probe non perturbative region. He was also able to show that QCD confines quarks in strong coupling expansion on a discrete space time lattice, but not in continuum limit. Numerical simulations however confirms that QCD accounts for quark Confinement, but we have yet to prove it analytically.
7. There are other questions to ask: does QCD explains hadron spectrum? New hadron predictions? Does QCD accounts for spontaneously broken chiral symmetry; it is believed that \(\pi^{0}\) is Goldstone boson resulted from spontaneously broken chiral symmetry. How does hadronic matter behave in high temperatures and high densities. Does QCD predicts phase transitions at some temperatures? This question is relevant for study of early universe. To answer all these questions one need non-perturbative QCD and lattice framework is only framework which provide non-perturbative treatment of QCD.