A nonsupersymmetric matrix orbifold

TL;DR

The paper develops a nonsupersymmetric matrix model for a twisted Type IIA setup with antiperiodic fermions on a spatial circle, realized as a $U(N)\times U(N)$ gauge theory with bifundamental fermions. It presents both local and nonlocal formulations and connects the construction to Type 0 theories via Scherk–Schwarz and dualities, yielding matrix-string limits that reproduce Rohm compactifications. However, the authors argue that the lack of SUSY nonrenormalization theorems and the lifting of moduli lead to instabilities and a breakdown of a Lorentz-invariant spacetime interpretation, casting doubt on the viability of a Lorentz-invariant vacuum in this nonsupersymmetric Matrix Theory. The work thus cautions about the limits of matrix-string constructions in nonsupersymmetric settings and highlights the intricate interplay between boundary conditions, dualities, and spacetime physics in M-theory compactifications.

Abstract

We construct the matrix description for a twisted version of the IIA string theory on S^1 with fermions antiperiodic around a spatial circle. The result is a 2+1-dimensional U(N) x U(N) nonsupersymmetric Yang-Mills theory with fermionic matter transforming in the (N,Nbar). The two U(N)'s are exchanged if one goes around a twisted circle of the worldvolume. Relations with Type 0 theories are explored and we find Type 0 matrix string limits of our gauge theory. We argue however that most of these results are falsified by the absence of SUSY nonrenormalization theorems and that the models do not in fact have a sensible Lorentz invariant space time interpretation.