Matrix Model Maps in AdS/CFT

TL;DR

This work extends the known AdS/CFT map from $1/2$-BPS states to a two-matrix quantum mechanics by introducing a hybrid collective-field/coherent-state framework with impurity degrees of freedom, yielding a two-parameter spectrum and a closed operator structure. It constructs a two-dimensional kernel that provides a one-to-one correspondence between matrix-model eigenstates and linearized SUGRA fluctuations on $AdS\times S$, generalizing the LLM mapping to include radial dependence in both AdS and the sphere. In the BPS limit the map reduces to the familiar LLM kernel; away from BPS, the kernel implements a canonical transformation akin to those used in noncritical string theory, with an exclusion-principle-like cutoff ensuring loop-space closure. The results offer a principled route to reconstruct aspects of AdS quantum mechanics from matrix-model data and suggest directions for incorporating interactions beyond the harmonic oscillator potential and exploring coupling corrections.

Abstract

We discuss an extension of a map between between BPS states and free fermions. The extension involves states associated with a full two matrix problem which are constructed using a sequence of integral equations. A two parameter set of matrix model eigenstates is then related to states in SUGRA. Their wavefunctions are characterized by nontrivial dependence on the radial coordinate of AdS and of the Sphere respectively. A kernel defining a one to one map between these states is then constructed.