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Theoretical Physics
Abstract:
We construct a quantum mechanical matrix model that approximates N=1 super-Yang-Mills on S3×R. We do so by pulling back the set of left-invariant connections of the gauge bundle onto the real superspace, with the spatial R3 compactified to S3. We quantize the N=1 SU(2) matrix model in the weak-coupling limit 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.
