Noncommutative Yang-Mills in IIB Matrix Model

TL;DR

The work addresses how noncommutative Yang-Mills theory can be realized in a nonperturbative matrix-model setting. By proving an equivalence between NCYM and twisted reduced models and applying it to the IIB matrix model with D-brane backgrounds, the authors obtain NCYM theories in various dimensions (notably 2D ${\cal N}=8$ and 4D ${\cal N}=4$) and demonstrate how spacetime coordinates emerge from matrices. They analyze D-instanton configurations and their interactions, showing consistency with gauge theory at short range and with IIB supergravity at large separations, thereby illustrating a gauge/gravity unification within a single framework. The results provide a concrete, nonperturbative avenue to study NCYM, D-brane dynamics, and gravity, with implications for the Maldacena conjecture and Seiberg–Witten noncommutativity in a matrix-model setting.

Abstract

We show that twisted reduced models can be interpreted as noncommutative Yang-Mills theory. Based upon this correspondence, we obtain noncommutative Yang-Mills theory with D-brane backgrounds in IIB matrix model. We propose that IIB matrix model with D-brane backgrounds serve as a concrete definition of noncommutative Yang-Mills. We investigate D-instanton solutions as local excitations on D3-branes. When instantons overlap, their interaction can be well described in gauge theory and AdS/CFT correspondence. We show that IIB matrix model gives us the consistent potential with IIB supergravity when they are well separated.