Matrix at slow roll: Nonrelativistic and Perturbative

Abstract

We analyze the slow roll limit of the massive version of time-dependent Yang--Mills type matrix model. We find that this limit reproduces the one-loop non-Hermitian matrix model, describing the dilatations of the local gauge invariant composite operators in the scalar sector of $\mathcal{N}=4$ super Yang--Mills theory. This coincidence is explained through the fact that the dialtation operator of the last can be identified with the radial time Hamiltonian. Further we explore the finite mass corrections to the slow roll action. The regular corrections in large mass expansions are coming from the modes with frequencies smaller than the mass parameter of the theory.