Matrix Theory Compactification on Noncommutative $T^4/Z_2$

TL;DR

This paper constructs gauge bundles on a noncommutative $T^4/Z_2$ orbifold, explicitly finding solutions with constant curvature and analyzing the moduli space, advancing understanding of matrix theory compactifications.

Contribution

It provides explicit constructions of gauge bundles on noncommutative $T^4/Z_2$ and finds solutions analogous to Connes-Douglas-Schwarz, linking noncommutative geometry with matrix theory.

Findings

Constructed gauge bundles with constant curvature on noncommutative $T^4_ heta$.

Derived solutions for matrix theory compactified on $T^4_ heta/Z_2$.

Identified the Higgs branch moduli space as an orbifold $T^4/Z_2$.

Abstract

In this paper, we construct gauge bundles on a noncommutative toroidal orbifold $T^4_\theta/Z_2$. First, we explicitly construct a bundle with constant curvature connections on a noncommutative $T^4_\theta$ following Rieffel's method. Then, applying the appropriate quotient conditions for its $Z_2$ orbifold, we find a Connes-Douglas-Schwarz type solution of matrix theory compactified on $T^4_\theta/Z_2$. When we consider two copies of a bundle on $T^4_\theta$ invariant under the $Z_2$ action, the resulting Higgs branch moduli space of equivariant constant curvature connections becomes an ordinary toroidal orbifold $T^4/Z_2$.