A Matrix Theory Construction of the IIA/IIB Wall

Abstract

In this note, we give a non-perturbative construction of a lightlike domain wall separating IIA and IIB string theories in 10D in the framework of discrete light-cone quantization (DLCQ). In this setting, generalizations of the BFSS conjecture relate the 10D flat space limit to matrix string theories (MSTs) for IIA and IIB. The former is equivalent to the large-$N$ limit of 2D Super Yang-Mills theory, while the latter is the large-$N$ limit of 3D ABJM theory with $\pm 1$ Chern-Simons levels. Our construction requires the string coupling to vanish at the location of the wall, and we show that BPS IIA $D0$-branes become non-BPS IIB $D0$-branes as they cross it, as anticipated in \cite{Heckman:2025wqd}.

Figures (4)

• Figure 1: Matrix string theory construction of IIA/IIB wall. The $(-1)^{F_L}_{IIA}$ symmetry of the symmetric orbifold CFT in the IIA $g_s=0$ region is gauged to the right of the red line. The $g_s>0$ regions correspond to turning on certain irrelevant deformations of the 2D symmetric orbifold SCFTs. On the IIA side, this irrelevant deformation corresponds to flowing away from $g_{YM}^2=\infty$ to finite gauge coupling. On the IIB side, the irrelevant deformation corresponds to a 2D $\rightarrow$ 3D decompactification.
• Figure 2: 10D Minkowski spacetime illustration of IIA/IIB wall located at $X^+=X^+_0$. In DLCQ coordinates, this is located at $\tau=\tau_0$. Between the purple lines indicates a region where the Einstein frame curvature is of the order of the string mass scale. See section \ref{['ssec:spacetimepic']} for more details.
• Figure 3: Symmetric orbifold configuration on $\mathbb{R}_\tau\times S^1_\sigma$ dual to a BPS IIA $D0$-brane localized along $X^-$. We have conformal interfaces (blue lines) separating the symmetric orbifold from the gapped $D0$-brane vacuum. The black lines are identified. The orange lines represent a single GS string with Dirichlet boundary conditions on the interfaces. These conformal interfaces are the IR limit of $U(N)$ Wilson lines in conjugate representations. Not pictured is are the overall gappless degrees of freedom in the $D0$ vacuum from the spin-0 and spin-1/2 components of the overall $U(1)$ vectormultiplet.
• Figure 4: 2D State-operator correspondence between a non-genuine local operator with a symmetry operator $\mathcal{U}$ attached and a state in a (topological) defect Hilbert space.