Moduli spaces of maximally supersymmetric solutions on noncommutative tori and noncommutative orbifolds

TL;DR

This paper investigates the structure of moduli spaces of constant curvature connections on noncommutative tori and orbifolds, revealing their relation to brane configurations in string theory.

Contribution

It provides a detailed analysis of equivariant moduli spaces on noncommutative tori and orbifolds, extending the understanding of supersymmetric solutions in noncommutative gauge theories.

Findings

Moduli spaces correspond to brane configurations on noncommutative spaces.

Explicit results for Z2 and Z4 orbifolds match commutative descriptions.

Equivariant connections satisfy additional orbifold constraints.

Abstract

A maximally supersymmetric configuration of super Yang-Mills living on a noncommutative torus corresponds to a constant curvature connection. On a noncommutative toroidal orbifold there is an additional constraint that the connection be equivariant. We study moduli spaces of (equivariant) constant curvature connections on noncommutative even-dimensional tori and on toroidal orbifolds. As an illustration we work out the cases of Z_{2} and Z_{4} orbifolds in detail. The results we obtain agree with a commutative picture describing systems of branes wrapped on cycles of the torus and branes stuck at exceptional orbifold points.