Matrix at slow roll: Nonrelativistic and Perturbative

TL;DR

This paper investigates the slow roll limit of a massive Yang--Mills matrix model, revealing its connection to the one-loop non-Hermitian matrix model and exploring finite mass corrections relevant to gauge theory dilatations.

Contribution

It demonstrates that the slow roll limit reproduces the one-loop dilatation operator of $ ext{N}=4$ SYM and analyzes finite mass corrections in this regime.

Findings

The slow roll limit matches the one-loop non-Hermitian matrix model.

Finite mass corrections originate from low-frequency modes.

The dilatation operator is identified with the radial time Hamiltonian.

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.