 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-354/1/b/i/solution

Δ = 2

in a boundary theory of dimension

d = 3

m^{2} = Δ (Δ - d) = - 2

in unit-radius

AdS_{4}

. In Poincare coordinates,

d s^{2} = \frac{1}{z ^{2}} (η_{μν} d x^{μ} d x^{ν} + d z^{2}),

[z^{2} (\partial_{z}^{2} + □_{2 + 1}) - 2 z \partial_{z} + 2] ϕ = 0 .

ϕ (x, z) = z ψ (x, z)

therefore maps the equation to the flat half-space wave equation

(\partial_{z}^{2} + □_{2 + 1}) ψ = 0, z > 0 .

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