Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-307/4/iv/solution

In the proposed Spin(8) theory, the gaugino contributes to the mixed gauge-R anomaly. The fields have superfield R-charge one, so their fermions contribute zero. The spinor has fermion R-charge and index one, giving . The singlets and do not enter the gauge anomaly. Hence
and the proposed R-symmetry survives quantization.

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