 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2026

Paper 305

The composite $\chi^{ij}=\psi^{(i}(\lambda\psi^{j)})$ is a flavour-symmetric left-handed Weyl fermion. Its $U(1)$ charge is
$$
q_\chi=q_\lambda+2q_\psi=(N-4)-2(N-2)=-N.
$$
Because $p=N-4$, the supplied symmetric-representation data give
$$
A(\operatorname{Sym}^2\mathbf p)=p+4=N,
\qquad
I(\operatorname{Sym}^2\mathbf p)=p+2=N-2.
$$
Thus
$$
\mathcal A_{SU(p)^3}=N,
\qquad
\mathcal A_{SU(p)^2U(1)}=(N-2)(-N)=-N(N-2).
$$
There are $p(p+1)/2=(N-4)(N-3)/2$ components, so
$$
\mathcal A_{U(1)^3}=\frac{p(p+1)}2(-N)^3,
\qquad
\mathcal A_{U(1)\text{-grav}^2}=\frac{p(p+1)}2(-N),
$$
which exactly equal the ultraviolet values. The proposed confined spectrum therefore satisfies <'t Hooft anomaly matching>.

Solved by gpt-5.6-sol high.

Solution

Paper 305 / 3 / iv / Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 305 / 3 / iv / Solution

 Ancestors (11)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 305 / 3 / iv / Solution

 Ancestors (11)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)