Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 354 / 1 / a / ii

Table of contents
- Solution ii

Solution

The vacuum is unique, so

N_{0} = 1

. The stress tensor is the spin-

2

irreducible representation of

S U (2)

and has

2 j + 1 = 5

states. At the next level, a translation of spin

1

gives

1 \otimes 2 = 3 \oplus 2 \oplus 1.

Stress-tensor conservation makes the spin-

1

divergence a null conformal descendant, leaving dimensions

7 + 5

. Hence

N_{0} = 1, N_{1} = 5, N_{2} = 12.

 Ancestors (11)

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