Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 307 / 4 / vi

Only the $p$ Spin(8) vectors $q$ and the one spinor $t$ contribute to the magnetic gauge beta function. The supplied indices giveThe magnetic theory is infrared free when $b_0^{\mathrm{magnetic}}<0$, namelyAt $N=13$ the one-loop coefficient vanishes and higher-order dynamics decides the flow. For $N>13$, Seiberg duality says that the strongly coupled low-energy limit of the asymptotically free electric $SU(N)$ theory is described by the weakly coupled Spin(8) fields and the superpotential from part v.