Plane-wave Matrix Theory from N=4 Super Yang-Mills on RxS^3

TL;DR

This paper shows how a specific plane-wave matrix theory can be derived from four-dimensional N=4 Super Yang-Mills theory on a three-sphere via Kaluza-Klein reduction, linking it to conformal field theory operators.

Contribution

It demonstrates the origin of the plane-wave matrix theory from higher-dimensional Super Yang-Mills through a consistent truncation and explores its relation to the conformal field theory's dilatation operator.

Findings

Plane-wave matrix theory arises from N=4 SYM on S^3 via truncation.

One-loop scalar operator anomalous dimensions are captured by the matrix theory.

Two-loop results show the approximation breaks down at higher order.

Abstract

Recently a mass deformation of the maximally supersymmetric Yang-Mills quantum mechanics has been constructed from the supermembrane action in eleven dimensional plane-wave backgrounds. However, the origin of this plane-wave matrix theory in terms of a compactification of a higher dimensional Super Yang-Mills model has remained obscure. In this paper we study the Kaluza-Klein reduction of D=4, N=4 Super Yang-Mills theory on a round three-sphere, and demonstrate that the plane-wave matrix theory arises through a consistent truncation to the lowest lying modes. We further explore the relation between the dilatation operator of the conformal field theory and the hamiltonian of the quantum mechanics through perturbative calculations up to two-loop order. In particular we find that the one-loop anomalous dimensions of pure scalar operators are completely captured by the plane-wave matrix theory. At two-loop level this property ceases to exist.