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

Abstract

In this paper, we construct gauge bundles on a noncommutative toroidal orbifold $T_{\theta }^4/Z_2$. First, we explicitly construct a bundle with constant curvature connections on a noncommutative $T_{\theta }^4$ 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 $T_{\theta }^4/Z_2$. When we consider two copies of a bundle on $T_{\theta }^4$ invariant under the $Z_2$ action, the resulting Higgs branch moduli space of equivariant constant curvature connections becomes an ordinary toroidal orbifold $T^4/Z_2$.

19 pages, LaTeX, review part shortened and corrected

References in corpus (3)

• A Short Survey of Noncommutative Geometry
• Compactification of M(atrix) theory on noncommutative toroidal orbifolds
• Twisted Bundles on Noncommutative $T^4$ and D-brane Bound States

Cited by in corpus (3)

• Noncommutative K3 Surfaces
• Theta functions on Noncommutative T^4
• N-Point Deformation of Algebraic K3 Surfaces