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arXiv · 2511.21851

ADE Minimal Strings and Multi-Matrix Duals

Victor A. Rodriguez·Mykhaylo Usatyuk·Zi-Yue Wang
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Abstract

We revisit ADE minimal string theories, focusing on the D- and E-series minimal models coupled to Liouville theory. Unlike the A-series, whose duals are solvable two-matrix models, these theories are conjectured to correspond to unsolvable four-matrix integrals. We compute sphere four-point and torus one-point amplitudes in the AMS, DMS, and EMS via direct numerical integration over moduli space, confirming/disproving some known results and providing new data where matrix-model predictions are unavailable. From amplitudes with conformal boundaries, we find evidence for multi-matrix structure in the D-series, including scaled ramp behavior in cylinder diagrams and deviations from the ZZ-instanton sector of two-matrix models. We also perform a preliminary positivity bootstrap to constrain critical points of the multi-matrix models relevant to the DMS string.

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Victor A. Rodriguez, Mykhaylo Usatyuk, Zi-Yue Wang. 2025-11-26. ADE Minimal Strings and Multi-Matrix Duals. https://arxiv.org/abs/2511.21851

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