SL(2,R) matrix model and supersymmetric Yang-Mills integrals

TL;DR

This paper constructs a matrix model that replicates the power-law tail behavior of supersymmetric Yang-Mills integrals, revealing invariance under SL(2,R) transformations and connections to AdS space physics.

Contribution

We develop a matrix model that exactly reproduces the power-law tails of supersymmetric Yang-Mills integrals and demonstrate its invariance under SL(2,R) transformations.

Findings

Matrix model exhibits power-law tails independent of N

Eigenfunctions are invariant under SL(2,R) transformations

Model relates to wave functions in AdS space

Abstract

The density of states of Yang-Mills integrals in the supersymmetric case is characterized by power-law tails whose decay is independent of N, the rank of the gauge group. It is believed that this has no counterpart in matrix models, but we construct a matrix model that exactly exhibits this property. In addition, we show that the eigenfunctions employed to construct the matrix model are invariant under the collinear subgroup of conformal transformations, SL(2,R). We also show that the matrix model itself is invariant under a fractional linear transformation. The wave functions of the model appear in the trigonometric Rosen-Morse potential and in free relativistic motion on AdS space.