Born-Oppenheimer quantization of the matrix model for N=1 super-Yang-Mills theory

Abstract

We construct a quantum mechanical matrix model that is a dimensional reduction of N ¼ 1 super-Yang-Mills on S 3 × R. We do so by pulling back the set of left-invariant connections of the gauge bundle onto the real superspace, with the spatial R 3 compactified to S 3. We quantize the N ¼ 1 SUð2Þ matrix model in the weak-coupling limit g ≪ 1, with g the dimensionless gauge coupling constant, using the Born-Oppenheimer approximation and find that different superselection sectors emerge for the effective gluon dynamics in this regime, reminiscent of different phases of the full quantum theory. We demonstrate that the Born-Oppenheimer quantization is indeed compatible with supersymmetry, albeit in a subtle manner. In fact, we can define effective supercharges that relate the different sectors of the matrix model's Hilbert space. These effective supercharges have a different definition in each phase of the theory.

Axial Anomaly in the $SU(N)$ Gauge Matrix Model

“…We consider here the case of adjoint Weyl fermions, which are relevant for supersymmetric gauge matrix models [26]. We show that in this case too, there is a non-trivial index of Dirac operator in the instanton background, and hence, an anomaly.…”