N=4 super Yang-Mills matrix integrals for almost all simple gauge groups

TL;DR

This paper computes the partition function of N=4 super Yang-Mills matrix theory for various simple gauge groups, providing explicit values and conjectured formulas for classical groups and boundary terms related to the Witten index.

Contribution

It presents explicit calculations for classical and some exceptional gauge groups, and proposes general formulas for classical groups of arbitrary rank, advancing understanding of super Yang-Mills matrix integrals.

Findings

Computed partition functions for classical groups up to rank 11.

Explicitly calculated for exceptional groups G_2, F_4, E_6.

Proposed conjectural formulas for B_r, C_r, D_r series.

Abstract

In this paper the partition function of N=4 D=0 super Yang-Mills matrix theory with arbitrary simple gauge group is discussed. We explicitly computed its value for all classical groups of rank up to 11 and for the exceptional groups G_2, F_4 and E_6. In the case of classical groups of arbitrary rank we conjecture general formulas for the B_r, C_r and D_r series in addition to the known result for the A_r series. Also, the relevant boundary term contributing to the Witten index of the corresponding supersymmetric quantum mechanics has been explicitly computed as a simple function of rank for the orthogonal and symplectic groups SO(2N+1), Sp(2N), SO(2N).