Supersymmetric Yang-Mills quantum mechanics in various dimensions

Supersymmetric Yang-Mills quantum mechanics (SYMQM) results from the dimensional reduction of the Yang-Mills field theory in D space-time dimensions to a single point in the D− 1 dimensional space. It can be also viewed as the effective quantum mechanics of zero momentum modes of the original theory [1]. These systems were first considered in 80’s [2] as simple models with supersymmetry [3]. Independently, zero-volume field theories (especially pure Yang-Mills) were employed as the starting point of the small volume expansion, which is an important theoretical tool complementary to early lattice calculations [4, 5, 6]. Later the models attracted a new wave of interest after the hypothesis of the equivalence, between the D = 10,SU(∞) SYMQM and a M-theory of D0 branes [7, 8, 9, 10]. In this talk some new results obtained for the D = 4 system with SU(2) gauge symmetry will be presented.