A Matrix Model Dual of Type 0B String Theory in Two Dimensions

TL;DR

This paper proposes a non-perturbative dual for type 0B string theory in two dimensions, realized as a one-dimensional hermitian matrix model with a $Z_2$-symmetric potential $U(T)=U(-T)$ and the tachyon field $T$ as the matrix degree of freedom on $N$ unstable D0-branes. The spectrum splits into NSNS (even) and RR (odd) sectors, mapped to parity-even and parity-odd operators in the matrix model, providing a concrete open-closed duality akin to holography. By matching perturbative closed-string S-matrix elements and D-brane emission amplitudes, the authors derive a dictionary between matrix-model operators (even vs odd) and NSNS/RR states, including leg factors that appear in two-dimensional super Liouville theory. They further connect rolling eigenvalues to brane decay and show that macroscopic loop operators reproduce open-string partition functions and annulus amplitudes, supporting a coherent matrix-model description of type 0B in two dimensions and outlining a $0A$ counterpart via brane-antibrane systems. Overall, the work extends the open-closed duality paradigm to fermionic two-dimensional strings and provides a concrete, perturbatively validated matrix-model framework with a stable vacuum due to the $Z_2$ symmetry.

Abstract

We propose that type 0B string theory in two dimensions admits a dual description in terms of a one dimensional bosonic matrix model of a hermitian matrix. The potential in the matrix model is symmetric with respect to the parity-like Z_2 transformation of the matrix. The two sectors in the theory, namely the NSNS and RR scalar sectors correspond to two classes of operators in the matrix model, even and odd under the Z_2 symmetry respectively. We provide evidence that the matrix model successfully reconstructs the perturbative S-matrix of the string theory, and reproduces the closed string emission amplitude from unstable D-branes. Following recent work in two dimensional bosonic string, we argue that the matrix model can be identified with the theory describing N unstable D0-branes in type 0B theory. We also argue that type 0A theory is described in terms of the quantum mechanics of brane-antibrane systems.