Single-trace realization conjecture for one-dimensional Dirac ensembles

Let $D$ be the Dirac operator in a formal Dirac ensemble of type $(1,0)$ or $(0,1)$, with coupling constants $t_j$ and partition function

$$Z = \int_{\mathcal{G}}e^{-\frac{{t_{2}}}{4}\operatorname{Tr} D^{2} - \sum_{j\geq}^{d} \frac{t_{j}}{2 j}\operatorname{Tr} D^{j}}dD.$$

Here $\mathcal{G}$ is the relevant Dirac-ensemble integration space, and $\mathcal{H}_N$ denotes the space of $N\times N$ Hermitian matrices. Single-trace realization conjecture. The coupling constants $t_j$ can be tuned so that the integral becomes

$$\int_{\mathcal{H}_{N}}e^{-\frac{N}{2}\operatorname{Tr} H^{2} - \sum_{j\geq}^{d} \frac{c_{j}}{ j}N\operatorname{Tr} H^{j}}dH,$$

where the new coupling constants $c_j$, expressed in terms of the $t_j$, can take any real values. This conjecture asserts that the coupling-constant space of these one-dimensional Dirac ensembles contains the corresponding single-trace matrix models, despite the shared coupling constants of the single- and multi-trace terms.