Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 307 / 3 / iv

Table of contents
- Solution iv

Solution

The composite

χ^{ij}

is in the two-index symmetric representation of

S U (p)

and has

q_{χ} = 2 q_{ψ} + q_{λ} = - N .

For that representation,

A (sym) = p + 4 = N, I (sym) = p + 2 = N - 2, dim (sym) = \frac{p ( p + 1 )}{2} .

Its anomalies are consequently

N, qq u a d - N (N - 2), qq u a d - \frac{1}{2} p (p + 1) N^{3}, qq u a d - \frac{1}{2} p (p + 1) N,

in the same order as part iii. Every anomaly matches, so confinement to the proposed massless composite is consistent with 't Hooft anomaly matching.

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