ADE Minimal Strings and Multi-Matrix Duals

TL;DR

This paper investigates ADE minimal string theories, especially D- and E-series, using numerical methods to analyze amplitudes and explore multi-matrix structures, revealing new insights beyond solvable models.

Contribution

It provides numerical amplitude calculations and evidence for multi-matrix structures in D-series minimal strings, extending understanding beyond the solvable A-series models.

Findings

Numerical amplitudes confirm some known results and provide new data.

Evidence for multi-matrix structures in D-series minimal strings.

Preliminary positivity bootstrap constrains critical points of multi-matrix models.

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.