D-particle bound states and generalized instantons

TL;DR

This paper calculates the index of supersymmetric quantum mechanical systems derived from super-Yang-Mills theories in various dimensions, revealing specific fractional results depending on the dimension and gauge group.

Contribution

It provides explicit formulas for the index in reduced super-Yang-Mills theories for different dimensions and gauge groups, extending understanding of D-particle bound states.

Findings

Index values are 1/N^2 for D=4,6.

Index sums over divisors for D=10.

Discussion includes the D=3 case.

Abstract

We compute the principal contribution to the index in the supersymmetric quantum mechanical systems which are obtained by reduction to 0+1 dimensions of $\mathcal{N}=1$, $D=4,6,10$ super-Yang-Mills theories with gauge group SU(N). The results are: ${1\over{N^{2}}}$ for $D=4,6$, $\sum_{d | N} {1\over{d^{2}}}$ for D=10. We also discuss the D=3 case.