Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-307/3/iv/solution

For , the infrared fields at the origin are the nine mesons and three baryons plus three antibaryons, for fifteen chiral multiplets. Every elementary quark superfield has R-charge , so its fermion has charge . In the ultraviolet there are twelve quark Weyl fermions and three adjoint gauginos. Hence the two anomalies are
Each meson or baryon superfield contains two quarks and has R-charge , so each composite fermion has charge . The unconstrained infrared fields therefore give
Both results agree, establishing the requested 't Hooft anomaly matching. This smooth composite description is the , example of s-confinement.

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