 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

2021

Paper 354

The <AdS scalar-field boundary asymptotics> are
$$
\phi(x,z)=z^{3-\Delta}J(x)+z^\Delta A(x)+\cdots
=zJ(x)+z^2A(x)+\cdots.
$$
Thus the <holographic dictionary> becomes especially simple for the flat field $\psi=\phi/z$:
$$
\boxed{J(x)=\lim_{z\to0}\frac{\phi(x,z)}z
=\psi(x,0)},
$$
$$
\boxed{\langle\mathcal O(x)\rangle
=(2\Delta-d)A(x)=A(x)
=\lim_{z\to0}\partial_z\left(\frac{\phi(x,z)}z\right)}
$$
up to the overall normalization chosen for the bulk action and possible local counterterms. The leading mode is the source and the normalizable subleading mode is the response.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 354 / 1 / b / ii / Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 354 / 1 / b / ii / Solution

 Ancestors (12)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 354 / 1 / b / ii / Solution

 Ancestors (12)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)