(Multi)Matrix Models and Interacting Clones of Liouville Gravity

TL;DR

This work constructs solvable toy models of interacting multi-string theories by coupling large-N matrix models through multi-trace operators and taking appropriate double-scaling limits, yielding a holographic description of $k$ coupled $c\le 1$ non-critical strings. The authors show that such deformations render the worldsheet theory non-local (NLST) while leaving a tractable spacetime interpretation, with results expressible via bilateral Laplace transforms of undeformed free energies. They relate these phenomena to AdS/CFT via mixed boundary conditions for dual fields and analyze the tree-level versus higher-genus behavior, clarifying when a Liouville-based interpretation suffices and when a genuine NLST framework is required. The paper also generalizes to matrix quantum mechanics and multi-way intersections, and discusses spacetime implications such as graviton mass generation and RG-driven dynamics, highlighting open problems and extensions toward non-perturbative definitions and open-string sectors.

Abstract

Large-N matrix models coupled via multitrace operators are used to define, via appropriate double-scaling limits, solvable models of interacting multi-string theories. It is shown that although such theories are non-local at the world-sheet level they have a simple description of the spacetime physics. Such theories share the main characteristics of similarly coupled higher-dimensional CFTs. An interpretation has been given in the past of similar continuum limits in terms of Liouville interactions that violate the Seiberg bound. We provide a novel interpretation of this relation which agrees with the current understanding of Liouville theory and analogous observations in the AdS/CFT correspondence.