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

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, $SL(2,\mathbb{R})$. 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 anti-de Sitter space.