Shaping up BPS States with Matrix Model Saddle Points

TL;DR

This paper analytically studies the probability distributions of wavefunctions in a matrix model representing 1/8 BPS states in N=4 SYM, revealing their dual supergravity solutions via saddle point analysis.

Contribution

It provides the first analytical saddle point solutions for matrix model wavefunctions describing 1/8 BPS states at large N, linking them to classical supergravity geometries.

Findings

Derived explicit saddle point hypersurfaces for eigenvalue densities.

Connected matrix model solutions to dual supergravity backgrounds.

Enhanced understanding of BPS state distributions in large-N limit.

Abstract

We provide analytical results for the probability distribution of a family of wavefunctions of a quantum mechanics model of commuting matrices in the large-N limit. These wavefunctions describe the strong coupling limit of 1/8 BPS states of N=4 supersymmetric Yang-Mills theory. Therefore, in the large-N limit, they should be dual to classical solutions of type IIB supergravity that asymptotically approach AdS5xS5. Each probability distribution can be described as the partition function of a matrix model (different wavefunctions correspond to different matrix model potentials) which we study by means of a saddle point approximation. These saddle point solutions are given in terms of (five-dimensional) hypersurfaces supporting density distributions of eigenvalues.