Matrix theories

Quantum field theory is a difficult subject because it is based on the concept of the path integral, which is difficult to define rigorously. However, for theories without space and time, the path integral becomes an ordinary integral over matrices. Surprisingly such matrix theories have deep connections to quantum field theories, string theories and more. In this project the student will verify the computation that shows that the so-named IKKT matrix model has maximal supersymmetry and, once that is done, the student could check how unique this theory is. Can one add more interactions that preserve maximal supersymmetry? This is an important question for many reasons. One of them being that the dimensional reduction of (maximal) supersymmetric Yang Mills theories in D dimensions over a D-dimensional torus leads to the IKKT Model. An unsolved problem is understanding the possible higher derivative term in the maximal superymmetric Yang Mills action. Whatever these terms are, they must reduce to simple traces of matrix products that preserve the supersymmetry of the original IKKT model. Certainly, it will be much easier to find such traces of matrix products and it will lead to potentially new insights into the possible higher derivative terms of SUSY Yang Mills theory. This is project for advanded undergrad or grad students in mathematics of theoretical physics.