Deconstructing Noncommutativity with a Giant Fuzzy Moose

TL;DR

This paper explores how D-branes in orbifold backgrounds with discrete torsion lead to emergent non-commutative geometries, providing a new framework for understanding noncommutative theories and their string theory realizations.

Contribution

It introduces a deconstruction approach using large quiver theories to realize noncommutative geometries and connects discrete torsion to physical noncommutativity.

Findings

Large quiver limit reproduces matrix theory of higher-dimensional D-branes.

Finite fuzzy moose theories regularize non-commutative theories.

Provides explicit string theory models of gauge theories on fuzzy tori.

Abstract

We argue that the worldvolume theories of D-branes probing orbifolds with discrete torsion develop, in the large quiver limit, new non-commutative directions. This provides an explicit `deconstruction' of a wide class of noncommutative theories. This also provides insight into the physical meaning of discrete torsion and its relation to the T-dual B field. We demonstrate that the strict large quiver limit reproduces the matrix theory construction of higher-dimensional D-branes, and argue that finite `fuzzy moose' theories provide novel regularizations of non-commutative theories and explicit string theory realizations of gauge theories on fuzzy tori. We also comment briefly on the relation to NCOS, (2,0) and little string theories.