Multi-matrix models and emergent geometry

TL;DR

This paper investigates how local geometric structures emerge in large N multi-matrix models at strong coupling, using solvable models and observables related to off-diagonal excitation masses, with implications for fuzzy spheres.

Contribution

It demonstrates how emergent geometry depends on mass terms regulating infrared divergences and applies the concept to fuzzy spheres, combining analytic and numerical methods.

Findings

Emergent geometry appears at strong coupling with a regulating mass term.

Off-diagonal excitation masses serve as indicators of emergent geometry.

Numerical methods complement analytic results in studying emergent structures.

Abstract

Encouraged by the AdS/CFT correspondence, we study emergent local geometry in large N multi-matrix models from the perspective of a strong coupling expansion. By considering various solvable interacting models we show how the emergence or non-emergence of local geometry at strong coupling is captured by observables that effectively measure the mass of off-diagonal excitations about a semiclassical eigenvalue background. We find emergent geometry at strong coupling in models where a mass term regulates an infrared divergence. We also show that our notion of emergent geometry can be usefully applied to fuzzy spheres. Although most of our results are analytic, we have found numerical input valuable in guiding and checking our results.