Quantum field theories arise as low energy effective descriptions in quantum many-body systems. Although strongly coupled quantum field theories are rather common, there is no systematic way of understanding those theories. In this talk, I will discuss two condensed matter systems where non-perturbative tools may shed some light on strongly correlated systems. In the first part, I will talk about a 2+1 dimensional lattice model where supersymmetry emerges at a quantum critical point. In the second part, I will discuss a 2+1 dimensional non-Fermi liquid state whose low energy effective theory is related to matrix/string theory.