Matrix Model Maps in AdS/CFT

TL;DR

This paper extends the matrix model map in AdS/CFT to include two-matrix states, relating them to supergravity states with complex radial dependencies through integral equations and a kernel mapping.

Contribution

It introduces a novel extension of the matrix model map to two-matrix problems, connecting eigenstates to supergravity states with detailed radial dependence.

Findings

Established a one-to-one kernel map between matrix model states and supergravity states.

Demonstrated the dependence of wavefunctions on AdS and Sphere radial coordinates.

Extended the BPS state mapping to more complex two-matrix configurations.

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.