Random Matrices in Quantum Field Theory

Random matrices, or Matrix models, make ubiquitous appearance in many areas of physics, in particular in Quantum Field Theory. Exact, non-perturbative results in Quantum Field Theory are very rare, and one often has to rely on various approximation schemes, such as Feynman perturbation theory. In some cases, however, the problem reduces to random matrices and can then be solved exactly without making any approximations. Results of this type have been used to put conjectured relationship between Quantum Fields and String Theory to rigorous tests.

I will review how random matrices arise in Quantum Field Theory, going from simple examples based on the Gaussian matrix model to more complicated, but still solvable matrix models arising in supersymmetric field theories via localization of path integrals.