appear from the type IIB matrix model. A general discussion on the Dirac equation implies that it is necessary to have zero modes in the 6-dimensional Dirac operator. In fact, we show that the block-diagonal structure (\[eq: correspondence\_MY\]) of the typical solutions can be regarded as the emergence of intersecting D-branes. Indeed we find that zero modes appear in the limit of infinite matrix size if the dimensionality of the branes is chosen appropriately.

the Dirac equation
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From the fermionic action (\[S\_f\]) of the type IIB matrix model, one obtains the 10-dimensional Dirac equation $$\label{eq: 10d_Dirac}
\Gamma^M {{\left[ A_M, \Psi \right]}}=0 \ ,$$ where $\Psi$ satisfies the Weyl condition $$\label{eq: chirality_in_10d}
\Gamma_\chi \Psi = \Psi$$ with the chirality operator $\Gamma_\chi$ in 10 dimensions. Here we decompose the 10-dimensional gamma matrices $\Gamma^M$ as $$\Gamma^\mu= \rho^\mu \otimes \mathbf{1} \ , \quad
\Gamma^a= \rho_\chi \otimes \gamma^a \ ,$$ where $\rho^\mu$ and $\gamma^a$ are the 4-dimensional and 6-dimensional gamma matrices, respectively. Note that the chirality operator $\Gamma_\chi$ is also decomposed as $$\Gamma_\chi = \rho_\chi \otimes \gamma_\chi \ ,$$ where $\rho_\chi$ and $\gamma_\chi$ are the chirality operators in 4 and 6 dimensions, respectively.

Suppose $\Psi$ is chiral in four dimensions meaning $$\label{eq: chirality_in_4d_Psi}
(\rho_\chi 